// I can do all things through Christ who strenghthens me
// Philippians 4:13
#include "bits/stdc++.h"
#include "vision.h"
using namespace std;
#define REP(i, j, k) for (int i = j; i < (k); i++)
#define RREP(i, j, k) for (int i = j; i >= (k); i--)
template <class T>
inline bool mnto(T &a, const T b) {return a > b ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T &a, const T b) {return a < b ? a = b, 1 : 0;}
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
#define ALL(x) x.begin(), x.end()
#define SZ(x) (int) x.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<ll> vll;
typedef tuple<int, int, int> iii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005;
const int MAXN = 200005;
int h, w, k;
void construct_network(int H, int W, int K) {
h = H, w = W; k = K;
if (k == 1 && h != 1 && w != 1) {
int hs = h * w;
REP (i, 0, h) {
vi v(w);
iota(ALL(v), i * w);
add_or(v);
}
int ws = hs + h;
REP (j, 0, w) {
vi v;
REP (i, 0, h) {
v.pb(i * w + j);
}
add_or(v);
}
vi hall;
REP (i, 0, h - 1) {
hall.pb(add_and({hs + i, hs + i + 1}));
}
int hb = add_or(hall);
vi wall;
REP (i, 0, w - 1) {
wall.pb(add_and({ws + i, ws + i + 1}));
}
int wb = add_or(wall);
{
vi v;
vi all;
vi pfx(w);
REP (i, 0, w) {
v.pb(ws + i);
pfx[i] = add_not(add_or(v));
}
v.clear();
vi sfx(w);
RREP (i, w - 1, 0) {
v.pb(ws + i);
sfx[i] = add_not(add_or(v));
}
all.pb(sfx[1]);
REP (i, 1, w - 1) {
all.pb(add_and({pfx[i - 1], sfx[i + 1]}));
}
all.pb(pfx[w - 2]);
hb = add_and({add_or(all), hb});
}
{
vi v;
vi all;
vi pfx(h);
REP (i, 0, h) {
v.pb(hs + i);
pfx[i] = add_not(add_or(v));
}
v.clear();
vi sfx(h);
RREP (i, h - 1, 0) {
v.pb(hs + i);
sfx[i] = add_not(add_or(v));
}
all.pb(sfx[1]);
REP (i, 1, h - 1) {
all.pb(add_and({pfx[i - 1], sfx[i + 1]}));
}
all.pb(pfx[h - 2]);
wb = add_and({add_or(all), wb});
}
add_or({hb, wb});
/*
vi v1, v2;
REP (i, 0, h) {
REP (j, 0, w) {
if (i + j & 1) {
v1.pb(i * w + j);
} else {
v2.pb(i * w + j);
}
}
}
int t1 = add_or(v1), t2 = add_or(v2);
add_and({wb, hb, t1, t2});
*/
return;
}
vi all;
REP (i, 0, h) {
REP (j, 0, w) {
if (max(h, w) > 30 && min(h, w) != 1 && j != 0) {
break;
}
vi v;
REP (ni, 0, h) {
if (abs(ni - i) > k) {
continue;
}
{
// abs(ni - i) + nj - j = k
// nj = k - abs(ni - i) + j
int nj = k - abs(ni - i) + j;
if (nj >= 0 && nj < w) {
v.pb(ni * w + nj);
}
}
}
if (v.empty()) {
continue;
}
int tmp = add_or(v);
all.pb(add_and({i * w + j, tmp}));
}
}
add_or(all);
}
