// Om Namah Shivaya
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x, y) ((x + y - 1) / (y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep1(i, n) for(int i = 1; i <= n; ++i)
#define rev(i, s, e) for(int i = s; i >= e; --i)
#define trav(i, a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a, b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a, b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "vision.h"
const int LOG = 9;
void construct_network(int n, int m, int k) {
// does row i contain guy?
rep(i,n){
vector<int> v;
rep(j,m){
v.pb(i*m+j);
}
add_or(v);
}
// does col j contain guy?
rep(j,m){
vector<int> v;
rep(i,n){
v.pb(i*m+j);
}
add_or(v);
}
int pos_0 = add_and({0, add_not(0)});
int pos_1 = add_or({0, add_not(0)});
auto add = [&](vector<int> sum, int b){
vector<int> res;
int carry = pos_0;
res.pb(add_xor({sum[0], b}));
carry = add_and({sum[0], b});
rep1(j,LOG-1){
res.pb(add_xor({sum[j], carry}));
carry = add_and({sum[j], carry});
}
return res;
};
vector<int> sum;
rep(j,LOG) sum.pb(pos_0);
int curr_xor = pos_0;
vector<int> toadd;
rep(i,n){
// sum += curr_xor
toadd.pb(curr_xor);
// curr_xor ^= val[i]
curr_xor = add_xor({curr_xor, n*m+i});
}
// note: if curr_xor = 1 at the end, then we dont add anything to sum (because both black cells are in the same row)
curr_xor = add_not(curr_xor);
trav(val,toadd){
val = add_and({val,curr_xor});
sum = add(sum,val);
}
curr_xor = pos_0;
toadd.clear();
rep(j,m){
// sum += curr_xor
toadd.pb(curr_xor);
// curr_xor ^= val[i]
curr_xor = add_xor({curr_xor, n*m+n+j});
}
// note: if curr_xor = 1 at the end, then we dont add anything to sum (because both black cells are in the same col)
curr_xor = add_not(curr_xor);
trav(val,toadd){
val = add_and({val,curr_xor});
sum = add(sum,val);
}
// check if sum = k
int eq = pos_1;
rep(bit,LOG){
int val = 0;
if(k & (1 << bit)){
val = pos_1;
}
else{
val = pos_0;
}
int xo = add_xor({sum[bit], val});
int curr_eq = add_not(xo);
eq = add_and({eq, curr_eq});
}
}
