#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "game.h"
int n, k;
VVI gp;
VVI trans;
VI mnt;
VI mxf;
void init(int N, int K) {n = N, k = K;
trans = gp = VVI(n);
replr(i, 0, k-2) {
gp[i].pb(i+1);
trans[i+1].pb(i);
}
mnt = VI(n, 2e9);
mxf = VI(n, -2e9);
rep(u, k) mnt[u] = mxf[u] = u;
}
bool verj;
void recalcmnt(int u) {
if (mxf[u] > mnt[u]) verj = true;
if (mxf[u] == mnt[u] && u >= k) verj = true;
for (int v : trans[u]) if (mnt[u] < mnt[v]) {
mnt[v] = mnt[u];
recalcmnt(v);
}
}
void recalcmxf(int u) {
if (mxf[u] > mnt[u]) verj = true;
if (mxf[u] == mnt[u] && u >= k) verj = true;
for (int v : gp[u]) if (mxf[u] > mxf[v]) {
mxf[v] = mxf[u];
recalcmxf(v);
}
}
int add_teleporter(int u, int v) {
if (u == v && u < k) return true;
verj = false;
gp[u].pb(v);
trans[v].pb(u);
if (mnt[v] < mnt[u]) {
mnt[u] = mnt[v];
recalcmnt(u);
}
if (mxf[u] > mxf[v]) {
mxf[v] = mxf[u];
recalcmxf(v);
}
if (verj) return true;
return false;
}
