Cod sursa(job #1708847)

Utilizator diac_paulPaul Diac diac_paul Data 28 mai 2016 00:18:47
Problema Padure2 Scor Ascuns
Compilator cpp Status done
Runda Marime 1.43 kb
#include <cstdio>
#include <cassert>
#include <algorithm>
#define NMAX 2000005
#define XMAX 1005
#define MOD 2000003
#define ll long long
using namespace std;
int L[XMAX], C[XMAX], I[XMAX], Nr[XMAX], F[NMAX];

bool comp(int i, int j) {
	return L[i] < L[j] || (L[i] == L[j] && C[i] < C[j]);
}

int inv(int a) {
	int ans = 1;
	for(int n = MOD - 2; n; n >>= 1) {
		if (n & 1)
			ans = (ll)ans * a % MOD;
		a = (ll)a * a % MOD;
	}
	return ans;
}

int f(int n, int m) {
	return (ll)F[n + m] * inv(F[n]) % MOD * inv(F[m]) % MOD;
}

int main() {
	int n, m, x;
	freopen("grader_test12.in", "r", stdin);
	freopen("grader_test12.ok", "w", stdout);
	scanf("%d%d%d", &n, &m, &x);
	assert(1 < n); assert(n <= 1000000);
	assert(1 < m); assert(m <= 1000000);
	assert(x <= 1000); assert(x <= (ll)n * m);
	
	--n; --m;
	for (int i = 0; i < x; ++i) {
		scanf("%d%d", L + i, C + i);
		--L[i]; --C[i];
		I[i] = i;
	}
	
	F[0] = 1;
	for (int i = 1; i < NMAX; ++i)
		F[i] = (ll)F[i - 1] * i % MOD;
	sort(I, I + x, comp);

	for (int i = 1; i < x; ++i)
		assert(L[I[i]] != L[I[i - 1]] || C[I[i]] != C[I[i - 1]]);

	int ans = f(n, m);
	for (int i = 0; i < x; ++i) {
		int invNr = MOD - (Nr[i] + f(L[I[i]], C[I[i]])) % MOD;
		ans = (ans + (ll)invNr * f(n - L[I[i]], m - C[I[i]])) % MOD;
		for (int j = i + 1; j < x; ++j)
			if (L[I[i]] <= L[I[j]] && C[I[i]] <= C[I[j]])
				Nr[j] = (Nr[j] + (ll)invNr * f(L[I[j]] - L[I[i]], C[I[j]] - C[I[i]])) % MOD;
	}
	printf("%d\n", ans);
	return 0;
}