いろはちゃんとマス目 / Iroha and a Grid （组合数学）

 1 #include <iostream>
 2 #include <algorithm>
 3 #include <cstring>
 4 #include <cstdio>
 5 #include <vector>
 6 #include <cstdlib>
 7 #include <iomanip>
 8 #include <cmath>
 9 #include <ctime>
10 #include <map>
11 #include <set>
12 #include <queue>
13 using namespace std;
14 #define lowbit(x) (x&(-x))
15 #define max(x,y) (x>y?x:y)
16 #define min(x,y) (x<y?x:y)
17 #define MAX 100000000000000000
18 #define MOD 1000000007
19 #define pi acos(-1.0)
20 #define ei exp(1)
21 #define PI 3.141592653589793238462
22 #define INF 0x3f3f3f3f3f
23 #define mem(a) (memset(a,0,sizeof(a)))
24 typedef long long ll;
25 ll gcd(ll a,ll b){
26     return b?gcd(b,a%b):a;
27 }
28 bool cmp(int x,int y)
29 {
30     return x>y;
31 }
32 const int N=2e5+20;
33 const ll mod=1e9+7;
34 ll f[N],n,m,A,B;
35 ll powmod(ll x,ll n)
36 {
37     ll s=1;
38     while(n){
39         if(n&1)
40             s=(s*x)%mod;
41         x=(x*x)%mod;
42         n>>=1;
43     }
44     return s;
45 }
46 ll C(ll n,ll m)
47 {
48     ll a=f[n];
49     ll b=(f[m]*f[n-m])%mod;
50     return (a*powmod(b,mod-2))%mod;
51 }
52 int main()
53 {
54     f[0]=1;
55     for(ll i=1;i<N;i++)
56         f[i]=(f[i-1]*i)%mod;
57     while(cin>>n>>m>>A>>B){
58         ll res=0;
59         for(ll i=B+1;i<=m;i++){
60             ll tmp=(C(i-1+n-A-1,n-A-1)*C(m-i+A-1,m-i))%mod;
61             res=(res+tmp)%mod;
62         }
63         cout<<res<<endl;
64     }
65     return 0;
66 }