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60 lines
1.4 KiB
C++
60 lines
1.4 KiB
C++
#include <iostream>
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#include <algorithm>
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#include <utility>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 1e5 + 5;
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const int mod = 1e9 + 7;
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int h, w, n, f[N];
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int fac[N << 1], inv[N << 1], fac_inv[N << 1];
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std::pair<int, int> a[N];
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inline int C(int n, int m) {
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return static_cast<long long>(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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fac[0] = 1;
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for (int i = 1; i < N << 1; i++) {
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fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
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}
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inv[0] = inv[1] = 1;
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for (int i = 2; i < N << 1; i++) {
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inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
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}
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fac_inv[0] = fac_inv[1] = 1;
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for (int i = 2; i < N << 1; i++) {
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fac_inv[i] = static_cast<long long>(fac_inv[i - 1]) * inv[i] % mod;
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}
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cin >> h >> w >> n;
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for (int i = 1, r, c; i <= n; i++) {
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cin >> a[i].first >> a[i].second;
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}
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std::sort(a + 1, a + 1 + n);
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a[n + 1] = std::make_pair(h, w);
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for (int i = 1; i <= n + 1; i++) {
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f[i] = C(a[i].first + a[i].second - 2, a[i].first - 1);
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for (int j = 1; j < i; j++) {
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f[i] = (f[i] - static_cast<long long>(f[j]) * C(a[i].first - a[j].first + a[i].second - a[j].second, a[i].first - a[j].first)) % mod;
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}
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}
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cout << (f[n + 1] + mod) % mod << endl;
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return 0;
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}
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