This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// #include "game.h"
#include <bits/stdc++.h>
using namespace std;
template<class T> using vec = vector<T>;
const int N = 3e5 + 2;
int n, k, tt[N][2];
vec<int> g[N][2];
void init(int n_, int k_) {
    n = n_ + 2, k = k_ + 2;
    for (int i = 0; i < n; i++)
        if (i < k)
            tt[i][0] = tt[i][1] = i;
        else
            tt[i][0] = 0, tt[i][1] = k - 1;
}
bool dfs(int i, int j, int t) {
    if (j < k)
        return 0;
    int p = tt[j][t];
    tt[j][t] = (t == 0 ? max(tt[i][t], tt[j][t]) : min(tt[i][t], tt[j][t]));
    if (tt[j][1] <= tt[j][0])
        return 1;
    if (__builtin_clz(p ^ tt[j][t ^ 1]) < __builtin_clz(tt[j][t] ^ tt[j][t ^ 1])) {
        for (int v : g[j][0])
            if (dfs(j, v, 0))
                return 1;
        for (int v : g[j][1])
            if (dfs(j, v, 1))
                return 1;
    }
    return 0;
}
int add_teleporter(int i, int j) {
    i = i < k - 2 ? i + 1 : i + 2;
    j = j < k - 2 ? j + 1 : j + 2;
    
    if (i < k && j < k)
        return i >= j;
    g[i][0].push_back(j), g[j][1].push_back(i);
    return dfs(i, j, 0) || dfs(j, i, 1);
}
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