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>
#define fi first
#define se second
#define all(v) (v).begin(), (v).end()
#define eb emplace_back
#define fastio ios::sync_with_stdio(false); cin.tie(NULL)
#define INF 2000000000;
#define LINF 1000000000000000000LL
#define mod 1000000007
using namespace std;
typedef long long ll;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
int r, c;
ll dp[55][55][55][55], fact[9090909];
ll f(int x1, int y1, int x2, int y2) {
if(x1 < 1 || y1 < 1 || x2 > r || y2 > c) return 0;
if(x1 == 1 && y1 == 1 && x2 == r && y2 == c) return 1;
if(dp[x1][y1][x2][y2] != 0) return dp[x1][y1][x2][y2];
dp[x1][y1][x2][y2] += (fact[x2-x1+1] * f(x1, y1, x2, y2+1)) % mod;
dp[x1][y1][x2][y2] += (fact[y2-y1+1] * f(x1, y1, x2+1, y2)) % mod;
dp[x1][y1][x2][y2] += (fact[x2-x1+1] * f(x1, y1-1, x2, y2)) % mod;
dp[x1][y1][x2][y2] += (fact[y2-y1+1] * f(x1-1, y1, x2, y2)) % mod;
dp[x1][y1][x2][y2] %= mod;
return dp[x1][y1][x2][y2];
}
int main() {
fastio;
int n, mx = 0, my = 0, mix = 3030, miy = 3030;
cin >> r >> c >> n;
fact[0] = 1;
for(int i = 1; i <= r * c; i++) {
fact[i] = (fact[i-1] * i) % mod;
}
for(int i = 1, x, y; i <= n; i++) {
cin >> x >> y;
mix = min(mix, x);
mx = max(mx, x);
miy = min(miy, y);
my = max(my, y);
}
cout << (f(mix, miy, mx, my) * fact[(mx-mix+1)*(my-miy+1)-n]) % mod;
}
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