This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define llint long long
void openFile() {
ios_base :: sync_with_stdio(false);
cin.tie(NULL);
#ifdef Tr___
freopen("test.inp", "r", stdin);
freopen("test.out", "w", stdout);
#else
//freopen("name.inp", "r", stdin);
//freopen("name.out", "w", stdout);
#endif
}
const int maxN = 3e3 + 5;
const int maxM = 1e6 + 5;
const llint INF = 1e9 + 7;
int N, R, C;
int xmin = INF, xmax = -INF, ymin = INF, ymax = -INF;
llint gt[maxN * maxN];
unordered_map<llint, llint> f;
void enter() {
cin >> R >> C;
cin >> N;
for (int i = 1; i <= N; ++i) {
int x, y;
cin >> x >> y;
xmin = min(xmin, x);
xmax = max(xmax, x);
ymin = min(ymin, y);
ymax = max(ymax, y);
}
}
inline llint getHash(int x, int y, int z, int t) {
return 1ll * (x - 1) * 10000 * 10000 * 10000
+ 1ll * (y - 1) * 10000 * 10000
+ 1ll * (z - 1) * 10000
+ 1ll * (t - 1);
}
llint getf(int xl, int xr, int yl, int yr) {
if (xl > xmin || xr < xmax) return 0;
if (yl > ymin || yr < ymax) return 0;
llint ha = getHash(xl, xr, yl, yr);
//cout << xl << " " << xr << " " << yl << " " << yr << " " << endl;
if (f.count(ha)) {
return f[ha];
}
llint res = 0;
res = (res + gt[xr - xl + 1] * getf(xl, xr, yl + 1, yr)) % INF;
res = (res + gt[xr - xl + 1] * getf(xl, xr, yl, yr - 1)) % INF;
res = (res + gt[yr - yl + 1] * getf(xl + 1, xr, yl, yr)) % INF;
res = (res + gt[yr - yl + 1] * getf(xl, xr - 1, yl, yr)) % INF;
f[ha] = res;
//cout << res << endl;
return res;
}
void solve() {
gt[0] = 1;
for (int i = 1; i <= R * C; ++i) {
gt[i] = gt[i - 1] * i % INF;
}
//cout << xmin << " " << xmax << " " << ymin << " " << ymax << endl;
f[getHash(xmin, xmax, ymin, ymax)] = gt[(xmax - xmin + 1) * (ymax - ymin + 1) - N];
//cout << getHash(xmin, xmax, ymin, ymax) << endl;
cout << getf(1, R, 1, C) << endl;
}
int main() {
openFile();
enter();
solve();
return 0;
}
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