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OI-codes/AtCoder/AGC001/E/E.cpp

71 lines
1.6 KiB
C++

#include <iostream>
#include <algorithm>
#include <cstring>
#include <iterator>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 2e5 + 5,
M = 2005;
const int mod = 1e9 + 7;
int n, m, a[N], b[N], inv[M << 2], fac[M << 2], inv_fac[M << 2], _f[M << 1][M << 1], *_pf[M << 1], **f, ans;
inline int C(int n, int m) {
return static_cast<long long>(fac[n]) * inv_fac[m] % mod * inv_fac[n - m] % mod;
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
fac[0] = 1;
for (int i = 1; i < M << 2; i++) {
fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
}
inv[0] = inv[1] = 1;
for (int i = 2; i < M << 2; i++) {
inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
}
inv_fac[0] = inv_fac[1] = 1;
for (int i = 2; i < M << 2; i++) {
inv_fac[i] = static_cast<long long>(inv_fac[i - 1]) * inv[i] % mod;
}
for (int i = 0; i < M << 1; i++) {
_pf[i] = _f[i] + M;
}
f = _pf + M;
cin >> n;
for (int i = 1; i <= n; i++) {
cin >> a[i] >> b[i];
f[-a[i]][-b[i]]++;
}
for (int i = -2000; i <= 2000; i++) {
for (int j = -2000; j <= 2000; j++) {
f[i][j] = (static_cast<long long>(f[i][j]) + f[i - 1][j] + f[i][j - 1]) % mod;
}
}
for (int i = 1; i <= n; i++) {
ans = (static_cast<long long>(ans) + f[a[i]][b[i]]) % mod;
}
for (int i = 1; i <= n; i++) {
ans = ((static_cast<long long>(ans) - C(2 * a[i] + 2 * b[i], 2 * a[i])) % mod + mod) % mod;
}
cout << (static_cast<long long>(ans) * inv[2] % mod) << endl;
return 0;
}