Petrozavodsk Winter Camp, Day 8, 2014, Rectangle Count

给一个n*m的格点图，问其中有多少个矩形？

$ sum_{x=1}^{nm} sum_{ab=x} [a + b leq n](n - a - b + 1)sum_{cd=x} [c + d leq m](m - c - bd + 1)$

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef long long ll;
#define rep(i, j, k) for (int i = int(j); i <= int(k); ++ i)
const int N = 2507;
LL f[N * N], g[N * N];

int main() {
    LL n, m;
    cin >> n >> m;
    n --; m --;
    rep(i, 1, n) rep(j, 1, n - i) 
        if (i * j < N * N) f[i * j] += (LL)(n - i - j + 1);
    rep(i, 1, m) rep(j, 1, m - i)
        if (i * j < N * N) g[i * j] += (LL)(m - i - j + 1);
    LL ans = 0;
    rep(i, 1, N * N - 1) {
        // if (f[i] * g[i]) cout << i << '
';
        ans += f[i] * g[i];
    }
    ans += (n * (n + 1) / 2) * (m * (m + 1) / 2);
    cout << ans << '
';     
}