bzoj2142 禮物

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擴展lucas 真nm難寫
只要會了就是板子題，，，，

CODE：

#include<cstdio>
#define N 100005
typedef long long ll;
struct node
{
    ll base,mod,ans;
}p[N];
int a[10];
int prime[N],num;
bool b[N];
ll mod,n,m,ans,sum,tot;
inline void eular()
{
    for(int i=2;i<=N-5;i++)
    {
        if(!b[i]) prime[++num]=i;
        for(int j=1;j<=num&&i*prime[j]<=N-5;j++)
        {
            b[i*prime[j]]=1;
            if(i%prime[j]==0) break;
        }
    }
}
inline void divide()
{
    ll tmp=mod;
    for(int i=1;i<=num&&tmp!=1;i++)
      if(tmp%prime[i]==0)
      {
        p[++tot].mod=1;
        p[tot].base=prime[i];
        while(tmp%prime[i]==0) tmp/=prime[i],p[tot].mod*=prime[i];
      }
}
inline ll ksm(ll a,ll b,ll mod)
{
    ll ans=1;
    for(;b;b>>=1,a=a*a%mod)
      if(b&1) ans=ans*a%mod;
    return ans;
}
void exgcd(ll a,ll b,ll &x,ll &y)
{
    if(!b){x=1,y=0;return;}
    exgcd(b,a%b,y,x),y-=x*(a/b);
}
inline ll inv(ll a,ll mod)
{
    ll t1,t2;
    exgcd(a,mod,t1,t2);
    return (t1%mod+mod)%mod;
}
void solve(int id,ll n,ll &x,ll &y)
{
    x=1,y=n/p[id].base;
    for(ll i=1;i<p[id].mod;i++)
      if(i%p[id].base) x=x*i%p[id].mod;
    x=ksm(x,n/p[id].mod,p[id].mod);
    for(ll i=n-n%p[id].mod+1;i<=n;i++)
      if(i%p[id].base) x=x*i%p[id].mod;
    ll t1,t2;
    if(y) solve(id,y,t1,t2),x=x*t1%p[id].mod,y+=t2;
}
inline ll crt()
{
    ll ans=0;
    for(int i=1;i<=tot;i++)
    {
        ll t1,t2;
        exgcd(p[i].mod,mod/p[i].mod,t1,t2);
        t2=(t2%mod+mod)%mod;
        ans=(ans+mod/p[i].mod*t2*p[i].ans)%mod;
    }
    return (ans%mod+mod)%mod;
}
int main()
{
    scanf("%lld%lld%lld",&mod,&n,&m);
    for(int i=1;i<=m;i++)
      scanf("%d",&a[i]),sum+=a[i];
    if(sum>n) return puts("Impossible"),0;
    if(sum<n) a[++m]=n-sum;
    eular(),divide();
    for(int i=1;i<=tot;i++)
    {
        ll t1,t2;
        solve(i,n,t1,t2);
        for(int j=1;j<=m;j++)
        {
            ll x,y;
            solve(i,a[j],x,y);t2-=y;
            t1=t1*inv(x,p[i].mod)%p[i].mod;
        }
        p[i].ans=t1*ksm(p[i].base,t2,p[i].mod)%p[i].mod;
    }
    printf("%lld",crt());
    return 0;
}