Luogu4640 BJWC2008 王之财宝 容斥、卢卡斯定理

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 
 4 inline int read(){
 5     int a = 0;
 6     bool f = 0;
 7     char c = getchar();
 8     while(c != EOF && !isdigit(c)){
 9         if(c == ‘-‘)
10             f = 1;
11         c = getchar();
12     }
13     while(c != EOF && isdigit(c)){
14         a = (a << 3) + (a << 1) + (c ^ ‘0‘);
15         c = getchar();
16     }
17     return f ? -a : a;
18 }
19 
20 const int MAXN = 100000;
21 int N , M , P , Q , jc[MAXN + 10] , ny[MAXN + 10] , B[16] , ans;
22 
23 inline int poww(long long a , int b){
24     int times = 1;
25     while(b){
26         if(b & 1)
27             times = times * a % Q;
28         a = a * a % Q;
29         b >>= 1;
30     }
31     return times;
32 }
33 
34 inline int C(int N , int M){
35     if(N < 0 || M < 0 || N < M)
36         return 0;
37     return 1ll * jc[N] * ny[M] % Q * ny[N - M] % Q;
38 }
39 
40 int lucas(int N , int M){
41     if(N + M == 0)
42         return 1;
43     return 1ll * C(N % Q , M % Q) * lucas(N / Q , M / Q) % Q;
44 }
45 
46 void choose(int now , int num , int cnt){
47     if(num < 0)
48         return;
49     if(now > M)
50         ans = (ans + (cnt & 1 ? -1ll : 1ll) * lucas(num + N , N) + Q) % Q;
51     else{
52         choose(now + 1 , num , cnt);
53         choose(now + 1 , num - B[now] - 1 , cnt + 1);
54     }
55 }        
56 
57 int main(){
58 #ifdef LG
59     freopen("4640.in" , "r" , stdin);
60 #endif
61     N = read();
62     M = read();
63     P = read();
64     Q = read();
65     jc[0] = ny[0] = 1;
66     for(long long i = 1 ; i < Q ; i++)
67         jc[i] = jc[i - 1] * i % Q;
68     ny[Q - 1] = poww(jc[Q - 1] , Q - 2);
69     for(long long i = Q - 2 ; i ; i--)
70         ny[i] = ny[i + 1] * (i + 1) % Q;
71     for(int i = 1 ; i <= M ; i++)
72         B[i] = read();
73     choose(1 , P , 0);
74     cout << ans;
75     return 0;
76 }