bzoj2142 礼物

 1 #include <bits/stdc++.h>
 2 #define il inline
 3 #define RG register
 4 #define ll long long
 5 
 6 using namespace std;
 7 
 8 ll a[10],m,n,pp,sum,ans,rhl;
 9 
10 il ll qpow(RG ll a,RG ll b,RG ll p){
11   RG ll ans=1;
12   while (b){
13     if (b&1) (ans*=a)%=p;
14     (a*=a)%=p,b>>=1;
15   }
16   return ans;
17 }
18 
19 il ll inv(RG ll a,RG ll p,RG ll pr){
20   return qpow(a,pr/p*(p-1)-1,pr);
21 }
22 
23 il ll get(RG ll n,RG ll p){
24   RG ll ans=0; for (;n;n/=p) ans+=n/p; return ans;
25 }
26 
27 il ll fac(RG ll n,RG ll p,RG ll pr){
28   if (!n) return 1; RG ll ans=qpow(pp,n/pr,pr);
29   for (RG ll i=2;i<=n%pr;++i) if (i%p) (ans*=i)%=pr;
30   return ans*fac(n/p,p,pr)%pr;
31 }
32 
33 il ll C(RG ll n,RG ll m,RG ll p,RG ll pr){
34   if (n<m) return 0; RG ll a,b,c,ans; pp=1;
35   for (RG ll i=2;i<=pr;++i) if (i%p) (pp*=i)%=pr;
36   ans=qpow(p,get(n,p)-get(m,p)-get(n-m,p),pr);
37   a=fac(n,p,pr),b=fac(m,p,pr),c=fac(n-m,p,pr);
38   (ans*=a*inv(b,p,pr)%pr*inv(c,p,pr)%pr)%=pr;
39   return ans*(rhl/pr)%rhl*inv(rhl/pr%pr,p,pr)%rhl;
40 }
41 
42 int main(){
43 #ifndef ONLINE_JUDGE
44   freopen("gift.in","r",stdin);
45   freopen("gift.out","w",stdout);
46 #endif
47   cin>>rhl>>n>>m;
48   for (RG ll i=1;i<=m;++i) cin>>a[i],sum+=a[i];
49   if (sum>n) puts("Impossible"),exit(0); ans=1;
50   for (RG ll i=1,P,res,pr;i<=m;++i){
51     P=rhl,res=0;
52     for (RG ll j=2;j*j<=P;++j){
53       if (P%j) continue; pr=1;
54       while (P%j==0) P/=j,pr*=j;
55       (res+=C(n,a[i],j,pr))%=rhl;
56     }
57     if (P!=1) (res+=C(n,a[i],P,P))%=rhl;
58     (ans*=res)%=rhl,n-=a[i];
59   }
60   cout<<ans; return 0;
61 }