hdu 5226 Tom and matrix (推公式，lucas)

直接求这个公式：

   
    ∑bi=aCki=Ck+1b+1−Ck+1a
   

lucas :

 Cmn≡Cm/pn/p⋅Cm%pn%p(mod p) 

因为p可能是小质素，这样超过阶乘p的阶乘会爆0。

#include<iostream>
#include<math.h>
#include<stdio.h>
#include<algorithm>
#include<string.h>
#include<vector>
#include<queue>
#include<map>
#include<set>
#define B(x) (1<<(x))
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int oo = 0x3f3f3f3f;
const ll OO = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;
#define lson rt<<1
#define rson rt<<1|1
void cmax(int& a, int b){ if (b>a)a = b; }
void cmin(int& a, int b){ if (b<a)a = b; }
void cmax(ll& a, ll b){ if (b>a)a = b; }
void cmin(ll& a, ll b){ if (b<a)a = b; }
void cmax(double& a, double b){ if (a - b < eps) a = b; }
void cmin(double& a, double b){ if (b - a < eps) a = b; }
void add(int& a, int b, int mod){ a = (a + b) % mod; }
void add(ll& a, ll b, ll mod){ a = (a + b) % mod; }
//const int MOD = 1e9 + 7;
const int maxn = 100005;
ll mod;
ll f[maxn], inv[maxn];

ll quick_pow(ll a, ll k){
	ll ans = 1;
	while (k){
		if (k & 1) ans = (ans*a) % mod;
		a = (a*a) % mod;
		k >>= 1;
	}
	return ans;
}

ll lucas(ll n, ll m){
	if (n<m) return 0;
	return f[n] * inv[m] % mod * inv[n - m] % mod;
}

ll C(ll n, ll m){
	if (!m) return 1;
	return lucas(n % mod, m % mod) * C(n / mod, m / mod) % mod;
}

int main(){
	int T, x1, x2, y1, y2, p;
	while (scanf("%d %d %d %d %d", &x1, &y1, &x2, &y2, &p) != EOF){
		mod = p;
		f[0] = inv[0] = 1;
		for (int i = 1; i < maxn; i++){
			f[i] = f[i - 1] * i%p;
			inv[i] = inv[i - 1] * quick_pow(i, mod - 2) % mod;
		}
		ll ans = 0;
		for (int i = y1; i <= y2; i++){
			ans += ((C(x2 + 1, i + 1) - C(x1, i + 1)) % mod + mod) % mod;
			ans %= mod;
		}
		ans = (ans%mod + mod) % mod;
		cout << ans << endl;
	}
	return 0;
}