131 lines
2.3 KiB
C++
131 lines
2.3 KiB
C++
#include<iostream>
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#include<cstdio>
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#include<string>
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#include<cstring>
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#include<algorithm>
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#include<cmath>
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using namespace std;
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typedef long long ll;
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const int maxn=100005;
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ll n,k,m;
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ll f1[2*maxn],f2[maxn],c[maxn],mul[maxn],num[maxn],tot;
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ll cp()
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{
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f1[0]=1%m;f1[1]=0;
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ll i;
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for(i=2;i<=2*m;++i)
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f1[i]=(((f1[i-1]+f1[i-2])%m)*(i-1))%m;
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return f1[(n-k)%(2*m)];
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}
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void prem()
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{
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ll i,mm;
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mm=m;
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tot=0;
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for(i=2;i*i<=mm;++i)
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{
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if(mm%i==0)
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{
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c[tot]=i;mul[tot]=1;num[tot]=0;
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while(mm%i==0)
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{
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mul[tot]*=i;
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num[tot]++;
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mm/=i;
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}
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tot++;
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}
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}
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if(mm!=1)
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{
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c[tot]=mm;mul[tot]=mm;num[tot]=1;
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tot++;
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}
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}
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ll quickpow(ll a,ll b,ll c)
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{
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ll ret=1;
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while(b)
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{
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if(b&1)
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{
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(ret*=a)%=c;
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}
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(a*=a)%=c;
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b>>=1;
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}
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return ret%c;
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}
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void ex_gcd(ll a,ll b,ll &x,ll &y)
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{
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if(b==0)
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{
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x=1;y=0;
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return ;
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}
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ex_gcd(b,a%b,x,y);
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ll t=x;
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x=y;
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y=t-(a/b)*y;
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}
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ll count(ll a,ll p)
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{
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if(a<p)
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return 0;
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else
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return a/p+count(a/p,p);
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}
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ll count2(ll a,ll p,ll mp)
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{
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if(a<p)
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return f2[a];
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return ((f2[a%mp]*quickpow(f2[mp-1],a/mp,mp))%mp*count2(a/p,p,mp))%mp;
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}
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ll work1(ll id)
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{
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ll p=c[id];ll mp=mul[id];ll nm=num[id];
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ll t1;
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t1=count(n,p)-count(k,p)-count(n-k,p);
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if(t1>=nm)
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return 0;
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ll ret=quickpow(p,t1,mp);
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ll i,x,y;
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f2[0]=1;
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for(i=1;i<=mp;++i)
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{
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f2[i]=f2[i-1];
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if(i%p!=0)
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f2[i]*=i;
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f2[i]%=mp;
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}
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ex_gcd(count2(k,p,mp)*count2(n-k,p,mp),mp,x,y);
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(ret*=x)%=mp;
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(ret*=count2(n,p,mp))%=mp;
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return ret;
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}
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ll work()
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{
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ll i,ret=0,tmp,x,y;
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prem();
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for(i=0;i<tot;++i)
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{
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tmp=work1(i);
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ex_gcd(m/mul[i],mul[i],x,y);
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ret+=(((m/mul[i])%m*x)%m*tmp)%m;
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}
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ret=(ret%m+m)%m;
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return (ret*cp())%m;
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}
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int main()
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{
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int t,cas=0;
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scanf("%d",&t);
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while(t--)
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{
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cas++;
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scanf("%I64d%I64d%I64d",&n,&k,&m);
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printf("Case %d: %I64d\n",cas,work());
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}
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return 0;
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}
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