#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#include "../../cpp/template/template.cpp"
#include "../../cpp/graph/tree/lowest-common-ancestor.cpp"
int main(){
int n,q;cin>>n>>q;
vector<vector<int>> edge(n);
for(int i = 0; n-1 > i; i++){
int x;cin>>x;
edge[x].push_back(i+1);
}
LCA lca(n, edge);
for(int i = 0; q > i; i++){
int u,v;cin>>u>>v;
cout << lca.compute(u,v) << endl;
}
}
#line 1 "cpp/z_test/yosupo-lca.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#line 2 "cpp/template/template.cpp"
//yukicoder@cpp17
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <cctype>
#include <climits>
#include <cassert>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <random>
#include <bitset>
#include <complex>
#include <utility>
#include <numeric>
#include <functional>
using namespace std;
using ll = long long;
using P = pair<ll,ll>;
const ll MOD = 998244353;
const ll MODx = 1000000007;
const int INF = (1<<30)-1;
const ll LINF = (1LL<<62LL)-1;
const double EPS = (1e-10);
P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}};
P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}};
template <typename T> vector<T> make_vector(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_vector(size_t a, Ts... ts) { return vector<decltype(make_vector(ts...))>(a, make_vector(ts...)); }
/*
確認ポイント
cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる
計算量は変わらないが楽できるシリーズ
min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる
count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる
*/
/* comment outed because can cause bugs
__attribute__((constructor))
void initial() {
cin.tie(0);
ios::sync_with_stdio(false);
}
*/
#line 4 "cpp/z_test/yosupo-lca.test.cpp"
#line 1 "cpp/data-structure/segment-tree/segment-tree.cpp"
template< typename T, typename F>
struct SegmentTree{
private:
int n;
vector<T> node;
F f;
T initer;
public:
SegmentTree(int n_, F f, T initer) : f(f),initer(initer) {
n = 1;
while(n < n_)n*=2;
node.resize(2*n-1, initer);
}
SegmentTree(int n_, F f,T initer, vector<T> x) : f(f),initer(initer) {
n = 1;
while(n < n_)n*=2;
node.resize(2*n-1, initer);
set(x);
}
void set(vector<T> x){
for(int i = 0; (int)x.size() > i; i++){
update(i,x[i]);
}
}
void update(int x, T val){
x += (n-1);
node[x] = val;
while(x > 0){
x = (x-1)/2;
node[x] = f(node[2*x+1],node[2*x+2]);
}
}
void add(int x, T val){
x += (n-1);
node[x] += val;
while(x > 0){
x = (x-1)/2;
node[x] = f(node[2*x+1],node[2*x+2]);
}
}
T getf(int a,int b, int k=0, int l=0, int r=-1){
if(r < 0){
r = n-1;
}
if(r < a || b < l){
return initer;
}
if(a <= l && r <= b){
return node[k];
}
T vl = getf(a,b,2*k+1,l,(l+r)/2);
T vr = getf(a,b,2*k+2,(l+r)/2+1,r);
return f(vl,vr);
}
void debug(){
int nw = 1;
int curr = 1;
cout << "---begin---" << endl;
for(int i = 0; 2*n-1 > i; i++){
cout << node[i] << " ";
if(nw == curr)cout << endl,nw *= 2, curr=1;
else curr++;
}
cout << "---end---" << endl;
}
};
template <typename T, typename F>
SegmentTree<T, F> get_segment_tree(int N, const F &f, T initer){
return SegmentTree<T,F>{N,f,initer};
}
template <typename T, typename F>
SegmentTree<T, F> get_segment_tree(int N, const F &f, T initer, vector<T> x){
return SegmentTree<T,F>{N,f,initer,x};
}
#line 2 "cpp/graph/tree/lowest-common-ancestor.cpp"
struct EulerTourForLCA {
int n;
vector<vector<int>> edge;
vector<pair<int, int>> timeline;
vector<pair<int,int>> stump;
vector<int> parent;
EulerTourForLCA(int n, vector<vector<int>> edge):
n(n), edge(edge), timeline(2*n, {-1, 0}), stump(n, {-1,-1}), parent(n, 0), lock(n, false) {}
void build(int top){
timer = 0;
lock.assign(n, false);
lock[top] = true;
dfs(top, 0);
}
const pair<int,int> operator[](int index){
return stump[index];
}
private:
vector<bool> lock;
int timer = 0;
void dfs(int vertex, int depth){
stump[vertex].first = timer;
timeline[timer].first = vertex;
timeline[timer].second = depth;
timer++;
for(int i = 0; (int)edge[vertex].size() > i; i++){
if(!lock[edge[vertex][i]]){
lock[edge[vertex][i]] = true;
parent[edge[vertex][i]] = vertex;
dfs(edge[vertex][i], depth+1);
}
}
stump[vertex].second = timer;
timeline[timer].first = parent[vertex];
timeline[timer].second = depth-1;
timer++;
}
};
struct LowestCommonAncestor {
int n;
vector<vector<int>> edge;
EulerTourForLCA et;
function<pair<int,int>(pair<int,int>, pair<int,int>)> RMQ = [](pair<int,int> a, pair<int,int> b){
if(a.second < b.second)return a;
return b;
};
//function<const pair<int,int>> RMQ = [](pair<int,int> a, pair<int,int> b){
//};
SegmentTree<pair<int,int>, decltype(RMQ)> st;
LowestCommonAncestor(int n, vector<vector<int>> edge):n(n), edge(edge), et(n, edge), st(2*n, RMQ, {n+1, n+1}){
et.build(0);
st.set(et.timeline);
}
int compute(int l, int r){
auto ls = et[l].first;
auto rs = et[r].first;
if(ls > rs)swap(ls, rs);
auto mn = st.getf(ls, rs);
return mn.first;
}
};
using LCA = LowestCommonAncestor;
#line 6 "cpp/z_test/yosupo-lca.test.cpp"
int main(){
int n,q;cin>>n>>q;
vector<vector<int>> edge(n);
for(int i = 0; n-1 > i; i++){
int x;cin>>x;
edge[x].push_back(i+1);
}
LCA lca(n, edge);
for(int i = 0; q > i; i++){
int u,v;cin>>u>>v;
cout << lca.compute(u,v) << endl;
}
}
cpp/z_test/yosupo-lca.test.cpp
cpp/geometry/two-points-distance.cpp