#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pb emplace_back
#define AI(i) begin(i), end(i)
template<class T> bool chmin(T &a, T b) { return b < a && (a = b, true); }
template<class T> bool chmax(T &a, T b) { return a < b && (a = b, true); }
#ifdef KEV
#define DE(args...) kout("[ " + string(#args) + " ] = ", args)
void kout() { cerr << endl; }
template<class T, class ...U> void kout(T a, U ...b) { cerr << a << ' ', kout(b...); }
template<class T> void debug(T l, T r) { while (l != r) cerr << *l << " \n"[next(l)==r], ++l; }
#else
#define DE(...) 0
#define debug(...) 0
#endif
#include "vision.h"
const int MAX_N = 300010;
vector<int> operator + (vector<int> a, vector<int> b) { a.insert(end(a), AI(b)); return a; }
void construct_network(int H, int W, int K) {
auto to_id = [&](int i, int j) {
return i * W + j;
};
auto valid = [&](int i, int j) {
return i >= 0 && i < H && j >= 0 && j < W;
};
vector<int> bits;
{
vector<int> f(H), pf(H), suf(H);
for (int i = 0;i < H;++i) {
vector<int> qp;
for (int j = 0;j < W;++j)
qp.pb(to_id(i, j));
f[i] = add_or(qp);
}
for (int i = 0;i+1 < H;++i) {
pf[i] = f[i];
if (i) pf[i] = add_or({pf[i-1], pf[i]});
}
for (int i = H-1;i > 0;--i) {
suf[i] = f[i];
if (i+1 < H) suf[i] = add_or({suf[i+1], suf[i]});
}
for (int i = 0;i+1 < H;++i)
bits.pb(add_and({pf[i], suf[i+1]}));
}
{
vector<int> f(W), pf(W), suf(W);
for (int i = 0;i < W;++i) {
vector<int> qp;
for (int j = 0;j < H;++j)
qp.pb(to_id(j, i));
f[i] = add_or(qp);
}
for (int i = 0;i+1 < W;++i) {
pf[i] = f[i];
if (i) pf[i] = add_or({pf[i-1], pf[i]});
}
for (int i = W-1;i > 0;--i) {
suf[i] = f[i];
if (i+1 < W) suf[i] = add_or({suf[i+1], suf[i]});
}
for (int i = 0;i+1 < W;++i)
bits.pb(add_and({pf[i], suf[i+1]}));
}
int mxv = bits.size(), wid = __lg(mxv) + 1;
int zero = add_xor({0, 0}), one = add_not(zero);
vector<int> a(wid, zero), b(wid, zero);
for (int i = 0;i < wid;++i)
if (K>>i&1) b[i] = one;
for (int i : bits) {
for (int j = 0;j < wid;++j) {
int ret = add_xor({i, a[j]});
i = add_and({i, a[j]});
a[j] = ret;
}
}
vector<int> res;
for (int i = 0;i < wid;++i)
res.pb(add_xor({a[i], b[i]}));
int x = add_or(res);
add_not(x);
}
