diff --git a/Codeforces/559/C/C.cpp b/Codeforces/559/C/C.cpp new file mode 100644 index 00000000..c68636b9 --- /dev/null +++ b/Codeforces/559/C/C.cpp @@ -0,0 +1,59 @@ +#include +#include +#include + +using std::cin; +using std::cout; +const char endl = '\n'; + +const int N = 1e5 + 5; +const int mod = 1e9 + 7; + +int h, w, n, f[N]; +int fac[N << 1], inv[N << 1], fac_inv[N << 1]; +std::pair a[N]; + +inline int C(int n, int m) { + return static_cast(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod; +} + +int main() { + std::ios::sync_with_stdio(false); + cin.tie(nullptr); + + fac[0] = 1; + for (int i = 1; i < N << 1; i++) { + fac[i] = static_cast(fac[i - 1]) * i % mod; + } + + inv[0] = inv[1] = 1; + for (int i = 2; i < N << 1; i++) { + inv[i] = static_cast(mod - (mod / i)) * inv[mod % i] % mod; + } + + fac_inv[0] = fac_inv[1] = 1; + for (int i = 2; i < N << 1; i++) { + fac_inv[i] = static_cast(fac_inv[i - 1]) * inv[i] % mod; + } + + cin >> h >> w >> n; + + for (int i = 1, r, c; i <= n; i++) { + cin >> a[i].first >> a[i].second; + } + + std::sort(a + 1, a + 1 + n); + + a[n + 1] = std::make_pair(h, w); + for (int i = 1; i <= n + 1; i++) { + f[i] = C(a[i].first + a[i].second - 2, a[i].first - 1); + + for (int j = 1; j < i; j++) { + f[i] = (f[i] - static_cast(f[j]) * C(a[i].first - a[j].first + a[i].second - a[j].second, a[i].first - a[j].first)) % mod; + } + } + + cout << (f[n + 1] + mod) % mod << endl; + + return 0; +}