66 lines
1.3 KiB
C++
66 lines
1.3 KiB
C++
#include<cstdio>
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#define sqrt __builtin_sqrt//#include<cmath>
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using namespace std;
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typedef long long LL;
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LL exgcd(LL a,LL b,LL &x,LL &y)
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{
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if(!b) { x=1; y=0; return a; }
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LL d=exgcd(b,a%b,y,x);
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y-=(a/b)*x;
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return d;
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}
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LL n,m,p;
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inline LL pow(LL a,LL b,LL mod)
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{
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LL res;
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for(res=1;b;b>>=1,a=a*a%mod) if(b&1) res=res*a%mod;
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return res;
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}
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inline LL inv(LL n,LL mod)
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{
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LL x,y;
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exgcd(n,mod,x,y);
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return (x%mod+mod)%mod;
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}
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inline LL fac(LL n,LL pi,LL pk)
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{
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if(!n) return 1;
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LL res=1;
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for(LL i=2;i<=pk;++i) if(i%pi) (res*=i)%=pk;
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res=pow(res,n/pk,pk);
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for(LL i=2;i<=n%pk;++i) if(i%pi) (res*=i)%=pk;
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return res*fac(n/pi,pi,pk)%pk;
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}
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inline LL CRT(LL b,LL mod) { return b*inv(p/mod,mod)%p*(p/mod)%p; }
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inline LL C(LL n,LL m,LL pi,LL pk)
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{
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LL up=fac(n,pi,pk),d1=fac(m,pi,pk),d2=fac(n-m,pi,pk);
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LL k=0;
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for(LL i=n;i;i/=pi) k+=i/pi;
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for(LL i=m;i;i/=pi) k-=i/pi;
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for(LL i=n-m;i;i/=pi) k-=i/pi;
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return up*inv(d1,pk)%pk*inv(d2,pk)%pk*pow(pi,k,pk)%pk;
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}
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LL exlucas(LL n,LL m)
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{
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LL res=0,tmp=p,pk;
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int mx=sqrt(p)+5;
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for(int i=2;i<=mx;++i)
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if(tmp%i==0)
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{
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pk=1; while(tmp%i==0) pk*=i,tmp/=i;
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(res+=CRT(C(n,m,i,pk),pk))%=p;
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}
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if(tmp>1) (res+=CRT(C(n,m,tmp,tmp),tmp))%=p;
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return res;
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}
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int main()
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{
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#ifdef local
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freopen("pro.in","r",stdin);
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#endif
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scanf("%lld%lld%lld",&n,&m,&p);
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printf("%lld\n",exlucas(n,m));
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return 0;
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}
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