#include "vision.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
int H,W,K;
int col_or[200];
int row_or[200];
int xbit_ans[200];
int notxbit_ans[200];
int ybit_ans[200];
int notybit_ans[200];
int distx[200];
int disty[200];
int bitx = 0;
int bity = 0;
int cell(int y, int x)
{
return W*y + x;
}
void get_x_bit(int bit)
{
vi used;
rep(i,W)
{
vi match;
rep2(j,i+1,W-1)
{
if((j-i) & (1 << bit))
{
match.pb(col_or[j]);
}
}
if(siz(match) == 0) continue;
int or_ = add_or(match);
used.pb(add_and({or_,col_or[i]}));
}
if(siz(used) == 0) return;
xbit_ans[bit] = add_or(used);
notxbit_ans[bit] = add_not(xbit_ans[bit]);
}
void get_y_bit(int bit)
{
vi used;
rep(i,H)
{
vi match;
rep2(j,i+1,H-1)
{
if((j-i) & (1 << bit))
{
match.pb(row_or[j]);
}
}
if(siz(match) == 0) continue;
int or_ = add_or(match);
used.pb(add_and({or_,row_or[i]}));
}
if(siz(used) == 0) return;
ybit_ans[bit] = add_or(used);
notybit_ans[bit] = add_not(ybit_ans[bit]);
}
void get_x_dist(int d)
{
vi used;
rep(bit,bitx+1)
{
if(d & (1 << bit))
{
used.pb(xbit_ans[bit]);
}
else
{
used.pb(notxbit_ans[bit]);
}
}
if(siz(used) == 0) return;
distx[d] = add_and(used);
}
void get_y_dist(int d)
{
vi used;
rep(bit,bity+1)
{
if(d & (1 << bit))
{
used.pb(ybit_ans[bit]);
}
else
{
used.pb(notybit_ans[bit]);
}
}
if(siz(used) == 0) return;
disty[d] = add_and(used);
}
void construct_network(int h, int w, int k)
{
H = h;
W = w;
K = k;
if(W != 0)
{
bitx = __lg(W-1);
}
else bitx = -1;
if(H != 0)
{
bity = __lg(H-1);
}
else bity = -1;
//cor_or
rep(i,W)
{
vi used;
rep(j,H) used.pb(cell(j,i));
col_or[i] = add_or(used);
}
//row_or
rep(i,H)
{
vi used;
rep(j,W) used.pb(cell(i,j));
row_or[i] = add_or(used);
}
rep(b,bitx+1) get_x_bit(b);
rep(b,bity+1) get_y_bit(b);
rep(i,W) get_x_dist(i);
rep(i,H) get_y_dist(i);
vi used;
rep(i,W)
{
if(i > k) continue;
if(W == 1)
{
if(K-i >= 0 && K-i < H)
{
used.pb(add_and({disty[K-i]}));
}
}
else if(H == 1)
{
if(i == K)
{
used.pb(add_and({distx[i]}));
}
}
else
{
if(K-i >= 0 && K-i < H)
{
used.pb(add_and({distx[i],disty[K-i]}));
}
}
}
if(siz(used) > 0)
{
add_or(used);
}
else
{
vi all_;
rep(i,H*W) all_.pb(i);
int xd = add_or(all_);
add_not({xd});
}
}
