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:heavy_check_mark: online_test/library-checker/lca_hld.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#include "competitive/std/std.hpp"
#include "competitive/tree/heavy_light_decomposition.hpp"
#include "competitive/std/io.hpp"
int main() {
    ll n,q;
    input(n,q);
    vi from, to, cost(n-1, 1);
    rep(i, n-1) {
        ll p;
        input(p);
        from.push_back(p);
        to.push_back(i+1);
    }
    Graph g(n, from, to, cost, true);
    seg_add<ll> seg(vl(n, 0));
    HeavyLightDecomposition hld(g, seg);
    rep(q) {
        ll u,v;
        input(u,v);
        print(hld.lca(u,v));
    }
}
#line 1 "online_test/library-checker/lca_hld.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#line 2 "competitive/std/std.hpp"
#include <bits/stdc++.h>
#ifndef LOCAL_TEST
#pragma GCC target ("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#endif // LOCAL_TEST
using namespace std;
// 型名の短縮
using ll = long long;
using pii = pair<int, int>; using pll = pair<ll, ll>;
using vi = vector<int>;  using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>;  using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;
template<typename T> vector<vector<T>> vv(int h, int w, T val = T()) { return vector(h, vector<T>(w, val)); }
template<typename T> vector<vector<vector<T>>> vvv(int h1, int h2, int h3, T val = T()) { return vector(h1, vector(h2, vector<T>(h3, val))); }
template<typename T> vector<vector<vector<vector<T>>>> vvvv(int h1, int h2, int h3, int h4, T val = T()) { return vector(h1, vector(h2, vector(h3, vector<T>(h4, val)))); }
template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;
// 定数の定義
constexpr double PI = 3.14159265358979323;
constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;
float EPS = 1e-8; double EPSL = 1e-16;
template<typename T> bool eq(const T x, const T y) { return x == y; }
template<> bool eq<double>(const double x, const double y) { return abs(x - y) < EPSL; }
template<> bool eq<float>(const float x, const float y) { return abs(x - y) < EPS; }
template<typename T> bool neq(const T x, const T y) { return !(eq<T>(x, y)); }
template<typename T> bool ge(const T x, const T y) { return (eq<T>(x, y) || (x > y)); }
template<typename T> bool le(const T x, const T y) { return (eq<T>(x, y) || (x < y)); }
template<typename T> bool gt(const T x, const T y) { return !(le<T>(x, y)); }
template<typename T> bool lt(const T x, const T y) { return !(ge<T>(x, y)); }
constexpr int MODINT998244353 = 998244353;
constexpr int MODINT1000000007 = 1000000007;
// 入出力高速化
struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;
// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((ll)(x).size())
#define rep1(n) for(ll dummy_iter = 0LL; dummy_iter < n; ++dummy_iter) // 0 から n-1 まで昇順
#define rep2(i, n) for(ll i = 0LL, i##_counter = 0LL; i##_counter < ll(n); ++(i##_counter), (i) = i##_counter) // 0 から n-1 まで昇順
#define rep3(i, s, t) for(ll i = ll(s), i##_counter = ll(s); i##_counter < ll(t); ++(i##_counter), (i) = (i##_counter)) // s から t まで昇順
#define rep4(i, s, t, step) for(ll i##_counter = step > 0 ? ll(s) : -ll(s), i##_end = step > 0 ? ll(t) : -ll(t), i##_step = abs(step), i = ll(s); i##_counter < i##_end; i##_counter += i##_step, i = step > 0 ? i##_counter : -i##_counter) // s から t まで stepずつ
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define repe(a, v) for(auto& a : (v)) // v の全要素（変更可能）
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod
#define sdiv(n, m) (((n) - smod(n, m)) / (m)) // 非負div
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
int Yes(bool b=true) { cout << (b ? "Yes\n" : "No\n"); return 0; };
int YES(bool b=true) { cout << (b ? "YES\n" : "NO\n"); return 0; };
int No(bool b=true) {return Yes(!b);};
int NO(bool b=true) {return YES(!b);};
template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };
template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };
template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };
template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };
template<typename T> vector<T> vec_slice(const vector<T>& a, int l, int r) { vector<T> rev; rep(i, l, r) rev.push_back(a[i]); return rev; };
template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };
template<typename T> bool in_range(const T& val, const T& s, const T& t) { return s <= val && val < t; };

template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }

// modでのpow
ll powm(ll a, ll n, ll mod=INFL) {
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = (res * a) % mod;
        if (n > 1) a = (a * a) % mod;
        n >>= 1;
    }
    return res;
}
// 整数Sqrt
ll sqrtll(ll x) {
    assert(x >= 0);
    ll rev = sqrt(x);
    while(rev * rev > x) --rev;
    while((rev+1) * (rev+1)<=x) ++rev;
    return rev;
}
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新（更新されたら true を返す）
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す）
int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } // xのd進数桁数
/**
 * @brief std.hpp
 * @docs docs/std/std.md
 */
#line 3 "competitive/graph/graph.hpp"
template <class Cost> struct Graph{
public:
    struct Edge {
        int to;
        Cost cost;
        Edge() {};
        Edge(int _to, Cost _cost) : to(_to), cost(_cost) {};
    };
    struct AdjacencyListRange{
        using iterator = typename std::vector<Edge>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)distance(begi, endi); }
        const Edge& operator[](int i) const { return begi[i]; }
    };
private:
public:
    vector<Edge> E;
    vector<int> I;
    int n;
    Graph() : n(0) {}
    Graph(int _n) : n(_n) {}
    Graph(int _n, const vector<int>& from, vector<int>& to, vector<Cost>& cost, bool rev = false) : n(_n) {
        vector<int> buf(n+1, 0);
        for(int i=0; i<(int)from.size(); i++){
            ++buf[from[i]];
            if (rev) ++buf[to[i]];
        }
        for(int i=1; i<=_n; i++) buf[i] += buf[i-1];
        E.resize(buf[n]);
        for(int i=(int)from.size()-1; i>=0; i--){
            int u = from[i];
            int v = to[i];
            Cost c = cost[i];
            E[--buf[u]] = Edge(v, c);
            if(rev) E[--buf[v]] = Edge(u, c);
        }
        I = move(buf);
    }
    AdjacencyListRange operator[](int u) const {
        return AdjacencyListRange{ E.begin() + I[u], E.begin() + I[u+1] };
    }
    int num_vertices() const { return n; }
    int size() const { return num_vertices(); }
    int num_edges() const { return E.size(); }
    Graph<Cost> reversed_edges() const {
        Graph<Cost> res;
        int _n = res.n = n;
        vi buf(n+1, 0);
        for(auto v : E) ++buf[v.to];
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.E.resize(buf[n]);
        for(int u=0; u<n; u++) for(auto v : operator[](u)) res.E[--buf[v.to]] = {u, v.cost};
        res.I = std::move(buf);
        return res;
    }
};
template <class T> ostream& operator<<(ostream& os, Graph<T> g) {
    bool first = true;
    rep(i, g.n) repe(e, g[i]) {
        if (first) first = false;
        else os << endl;
        os << i << "->" << e.to << ": " << e.cost;
    }
    return os;
}
/**
 * @brief graph.hpp
 * @docs docs/graph/graph.md
 */
#line 5 "atcoder/segtree.hpp"

#line 2 "atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder
#line 7 "atcoder/segtree.hpp"

namespace atcoder {

template <class S, S (*_op)(S, S), S (*_e)()> struct segtree {
  public:
    S (*op)(S, S) = _op;
    S (*e)() = _e;
    segtree() : segtree(0) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }
    explicit segtree(int n) : segtree(std::vector<S>(n, _e())) {}

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    void add(int p, S x) {
        assert(0 <= p && p < _n);
        (*this).set(p, (*this).get(p) + x);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

    int n() const {return (*this)._n;}

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder
#line 4 "competitive/data_structure/segtree.hpp"
template <typename S, S (*op)(S, S), S (*e)()> std::ostream& operator<<(std::ostream& os, const atcoder::segtree<S, op, e> seg) {
    int n = seg.n();
    rep(i, n) { os << seg.get(i); if (i != n-1) os << " "; }
    return os;
};
namespace segtree_internal {
    template<typename T> T op_max(T x, T y) { return x > y? x : y; }
    template<typename T> T op_min(T x, T y) { return x < y? x : y; }
    template<typename T> T op_add(T x, T y) { return x + y; }

    template<typename T> T e_max() { return -INFL; }
    template<> int e_max() { return -INF; }
    template<typename T> T e_min() { return INFL; }
    template<> int e_min() { return INF; }
    template<typename T> T e_add() { return 0; }
}
template<class S, S (*op)(S,S), S(*e)()> using segtree = atcoder::segtree<S, op, e>;
template<typename T> using seg_add = segtree<T, segtree_internal::op_add<T>, segtree_internal::e_add<T>>;
template<typename T> using seg_max = segtree<T, segtree_internal::op_max<T>, segtree_internal::e_max<T>>;
template<typename T> using seg_min = segtree<T, segtree_internal::op_min<T>, segtree_internal::e_min<T>>;
/**
 * @brief セグメント木（ラッパー）
 * @docs docs/data_structure/segtree.md
 */
#line 6 "atcoder/lazysegtree.hpp"

#line 8 "atcoder/lazysegtree.hpp"

namespace atcoder {

template <class S,
          S (*_op)(S, S),
          S (*_e)(),
          class F,
          S (*_mapping)(F, S),
          F (*_composition)(F, F),
          F (*_id)()>
struct lazy_segtree {
  public:
    S (*op)(S, S) = _op;
    S (*e)() = _e;
    S (*mapping)(F, S) = _mapping;
    F (*composition)(F, F) = _composition;
    F (*id)() = _id;
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, _e())) {}
    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    void add(int p, S x) {
        assert(0 <= p && p < _n);
        (*this).set(p, (*this).get(p) + x);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

    int n() {return (*this)._n;}

  private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};

}  // namespace atcoder
#line 4 "competitive/data_structure/lazysegtree.hpp"
template <typename S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
std::ostream& operator<<(std::ostream& os, atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> seg) {
    int n = seg.n();
    rep(i, n) { os << seg.get(i); if (i != n-1) os << " "; }
    return os;
};

namespace lsegtree_internal {
    template<typename T> struct AddNode {
        T value;
        ll size;
        AddNode() : value(T(0)), size(1) {};
        AddNode(T value, ll size) : value(value), size(size) {};
        friend ostream& operator<<(std::ostream& os, const AddNode<T> &n) { os << n.value; return os; };
    };

    template<typename T> T e_max() { return -INFL; }
    template<> int e_max() { return -INF; }
    template<typename T> T e_min() { return INFL; }
    template<> int e_min() { return INF; }
    template<typename T> AddNode<T> e_add() { return {0, 1}; }

    template<typename T> T op_max(T x, T y) { return x > y ? x : y; }
    template<typename T> T op_min(T x, T y) { return x < y ? x : y; }
    template<typename T> AddNode<T> op_add(AddNode<T> x, AddNode<T> y) { return {x.value + y.value, x.size + y.size}; }

    template<typename T> T id_radd(){ return 0; }
    template<typename T> T id_rupdate(){ return INFL; }
    template<> int id_rupdate(){ return INF; }

    template<typename T> AddNode<T> mapping_add_radd(T f, AddNode<T> x){ return {x.value + f * x.size, x.size}; }
    template<typename T> AddNode<T> mapping_add_rupdate(T f, AddNode<T> x){
        AddNode<T> rev = AddNode<T>(x);
        if(f != id_rupdate<T>()) rev.value = f * rev.size;
        return rev;
    }
    template<typename T> T mapping_radd(T f, T x){ return f+x; }
    template<typename T> T mapping_rupdate(T f, T x){ return (f == id_rupdate<T>() ? x : f); }

    template<typename T> T composition_radd(T f, T g){ return f+g; }
    template<typename T> T composition_rupdate(T f, T g){ return (f == id_rupdate<T>() ? g : f); }
}

template <typename S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
using lsegtree = atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>;
template<typename T> using lseg_add_radd = atcoder::lazy_segtree<lsegtree_internal::AddNode<T>, lsegtree_internal::op_add<T>, lsegtree_internal::e_add<T>, T, lsegtree_internal::mapping_add_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;
template<typename T> using lseg_min_radd = atcoder::lazy_segtree<T, lsegtree_internal::op_min<T>, lsegtree_internal::e_min<T>, T, lsegtree_internal::mapping_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;
template<typename T> using lseg_max_radd = atcoder::lazy_segtree<T, lsegtree_internal::op_max<T>, lsegtree_internal::e_max<T>, T, lsegtree_internal::mapping_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;
template<typename T> using lseg_add_rupdate = atcoder::lazy_segtree<lsegtree_internal::AddNode<T>, lsegtree_internal::op_add<T>, lsegtree_internal::e_add<T>, T, lsegtree_internal::mapping_add_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;
template<typename T> using lseg_min_rupdate = atcoder::lazy_segtree<T, lsegtree_internal::op_min<T>, lsegtree_internal::e_min<T>, T, lsegtree_internal::mapping_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;
template<typename T> using lseg_max_rupdate = atcoder::lazy_segtree<T, lsegtree_internal::op_max<T>, lsegtree_internal::e_max<T>, T, lsegtree_internal::mapping_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;
/**
 * @brief 遅延セグメント木（ラッパー）
 * @docs docs/data_structure/lazysegtree.md
 */
#line 6 "competitive/tree/heavy_light_decomposition.hpp"
template <typename Cost, typename Seg> struct HeavyLightDecomposition {
    vi heavy_edge,in,out,head,par,pos;
    Seg &seg;
    bool edge;
    HeavyLightDecomposition(Graph<Cost>& g, Seg& seg, bool edge = true) :
        heavy_edge(g.n), in(g.n), out(g.n), head(g.n), par(g.n), pos(g.n), seg(seg), edge(edge) {
        build(g);
    }

    void build(Graph<Cost>& g) {
        vi subtree_size(g.n, 0);
        auto dfs_sz = [&] (auto self, int x, int p) -> int {
            par[x] = p;
            subtree_size[x] = 1;
            repe(e, g[x]) {
                if (e.to == p) continue;
                subtree_size[x] += self(self, e.to, x);
            }
            int maxs = -INF;
            heavy_edge[x] = -1;
            repe(e, g[x]) {
                if (e.to == p) continue;
                if (chmax(maxs, subtree_size[e.to])) heavy_edge[x] = e.to;
            }
            return subtree_size[x];
        };
        dfs_sz(dfs_sz, 0, -1);
        int t = 0;
        auto dfs_hld = [&] (auto self, int x, int par) -> void {
            in[x] = t++;
            pos[in[x]] = x;
            if (heavy_edge[x] != -1) {
                head[heavy_edge[x]] = head[x];
                self(self, heavy_edge[x], x);
            }
            repe(e, g[x]) {
                if (e.to == par || e.to == heavy_edge[x]) continue;
                head[e.to] = e.to;
                self(self, e.to, x);
            }
            out[x] = t;
        };
        dfs_hld(dfs_hld, 0, -1);
    }

    int lca(int u, int v) {
        while (head[u] != head[v]) {
            if (in[u] > in[v]) swap(u, v);
            v = par[head[v]];
        }
        return in[u] < in[v] ? u : v;
    }

    int la(int u, int k) {
        while (true) {
            if (u == -1) return -1;
            if (u == 0 && k > 0) return -1;
            int v = head[u];
            if (in[u] - k >= in[v]) return pos[in[u] - k];
            k -= in[u] - in[v] + 1;
            u = par[head[u]];
        }
    }

    decltype(seg.e()) prod(int u, int v) {
        using T = decltype(seg.e());
        T l = seg.e();
        T r = seg.e();
        while (head[u] != head[v]) {
            if (in[u] > in[v]) swap(u, v), swap(l, r);
            l = seg.op(seg.prod(in[head[v]], in[v] + 1), l);
            v = par[head[v]];
        }
        if (in[u] > in[v]) swap(u, v), swap(l, r);
        // パスクエリの場合はu（uからuの親へのパス）は足さない
        return seg.op(seg.op(seg.prod(in[u] + edge, in[v] + 1), l) , r);
    }

    template<typename F> void apply(int u, int v, F f) {
        while (head[u] != head[v]) {
            if (in[u] > in[v]) swap(u, v);
            seg.apply(in[head[v]], in[v] + 1, f);
            v = par[head[v]];
        }
        if (in[u] > in[v]) swap(u, v);
        seg.apply(in[u] + edge, in[v] + 1, f);
    }

    int edge_pos(int u, int v) {
        if (par[u] != v) swap(u, v);
        assert(par[u] == v);
        return in[u];
    }
};
/**
 * @brief HL分解 (Heavy Light Decomposition)
 * @docs docs/tree/heavy_light_decomposition.md
 */
#line 3 "competitive/std/io.hpp"
// 演算子オーバーロード（プロトタイプ宣言）
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p);
template <class T> inline istream& operator>>(istream& is, vector<T>& v);
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v);
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp);
template <typename T> ostream &operator<<(ostream &os, const set<T> &st);
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st);
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st);
template <typename T> ostream &operator<<(ostream &os, queue<T> q);
template <typename T> ostream &operator<<(ostream &os, deque<T> q);
template <typename T> ostream &operator<<(ostream &os, stack<T> st);
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq);

// 演算子オーバーロード
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repe(x, v) is >> x; return is; }
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st) { ll cnt = 0; for (auto &e : st) { os << e << (++cnt != (int)st.size() ? " " : ""); } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; }

template <typename T> int print_sep_end(string sep, string end, const T& val) { (void)sep; cout << val << end; return 0; };
template <typename T1, typename... T2> int print_sep_end(string sep, string end, const T1 &val, const T2 &...remain) {
    cout << val << sep;
    print_sep_end(sep, end, remain...);
    return 0;
};
template <typename... T> int print(const T &...args) { print_sep_end(" ", "\n", args...); return 0; };
template <typename... T> void flush() { cout << flush; };
template <typename... T> int print_and_flush(const T &...args) { print(args...); flush(); return 0; };
#define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print
template <typename T> void input(T &a) { cin >> a; };
template <typename T1, typename... T2> void input(T1&a, T2 &...b) { cin >> a; input(b...); };
#ifdef LOCAL_TEST
template <typename T> void debug_func(int i, const T name) { (void)i; (void)name; cerr << endl; }
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) {
    int scope = 0;
    for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {
        cerr << name[i];
        if (name[i] == '(' || name[i] == '{') scope++;
        if (name[i] == ')' || name[i] == '}') scope--;
    }
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, T2 &a, T3 &...b) {
    int scope = 0;
    for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {
        cerr << name[i];
        if (name[i] == '(' || name[i] == '{') scope++;
        if (name[i] == ')' || name[i] == '}') scope--;
    }
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
#endif
#ifndef LOCAL_TEST
template <typename... T>
void debug_func(T &...) {}
template <typename... T>
void debug_func(const T &...) {}
#endif
/**
 * @brief io.hpp
 * @docs docs/std/io.md
 */
#line 5 "online_test/library-checker/lca_hld.test.cpp"
int main() {
    ll n,q;
    input(n,q);
    vi from, to, cost(n-1, 1);
    rep(i, n-1) {
        ll p;
        input(p);
        from.push_back(p);
        to.push_back(i+1);
    }
    Graph g(n, from, to, cost, true);
    seg_add<ll> seg(vl(n, 0));
    HeavyLightDecomposition hld(g, seg);
    rep(q) {
        ll u,v;
        input(u,v);
        print(hld.lca(u,v));
    }
}
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