2 条题解

  • 6
    @ 2022-8-27 16:57:41
    /*****************************************
    备注:
    ******************************************/
    #include <queue>
    #include <math.h>
    #include <stack>
    #include <stdio.h>
    #include <iostream>
    #include <vector>
    #include <iomanip>
    #include <string.h>
    #include <algorithm>
    using namespace std;
    #define LL long long
    const int N = 1e5 + 10;
    const int mod = 999911659;
    LL num[N],len , n1[5] , inv[5];
    LL cc[5] = {0,2,3,4679,35617};
    LL power(LL a, LL b ,LL m)
    {
    	LL ans = 1;
    	while(b)
    	{
    		if(b&1)
    			ans = (ans * a) % m;
    		b >>= 1;
    		a = (a*a)%m;
    	}
    	return ans;
    }
    LL C(LL n , LL m , LL p)
    {
    	if(n < m)
    		return 0;
    	if(m < n-m)
    		m = n-m;
    	LL ans ,sum;
    	ans = sum = 1;
    	for(int i = 0 ; i < m ; i++)
    	{
    		ans = (ans * (n-i))%p;
    		sum = (sum * (i+1))%p;
    	}
    	return (ans * power(sum , p-2 , p) ) %p;
    }
    LL lucas(LL n , LL m , LL p)
    {
    	if(!m) return 1;
    	return (lucas(n/p , m/p , p) * C(n%p , m%p , p) )%p;
    }
    LL k[N];
    LL CRT()
    {
    	LL sums = 0;
    	for(int i = 1; i <= 4 ;i++)
    		sums = (sums + ((k[i]*n1[i])%(mod-1))*inv[i])%(mod-1);
    	return sums;
    }
    void init(LL n)
    {
    	for(int i = 1 ; i *i < n ; i++)
    		if(n%i == 0)
    			num[len++] = i , num[len++] = n/i;
    	LL p = sqrt(n);
    	if(p*p == n)
    		num[len++] = p;
    	LL nums = mod - 1;
    	for(int i = 1 ;i <= 4; i++)
    	{
    		n1[i] = nums/cc[i];
    		inv[i] = power(n1[i] , cc[i]-2 , cc[i]);
    	}
    }
    int main()
    {
    	LL n,q;
    	cin >> n >> q;
    	if(q%mod == 0)
    	{
    		cout << 0;
    		return 0;
    	}
    	init(n);
    	LL sum = 0;
    	for(int j = 1 ;j <= 4 ;j++)
    		for(int i = 0 ; i < len ; i++)
    			k[j] += lucas(n,num[i],cc[j]);
    	sum = CRT();
    	cout << power(q,sum,mod);
    	return 0;
    }
    
    • -2
      @ 2021-8-7 21:35:03

      C++ :

      
      #include<cstdio>
      #include<cstdlib>
      #include<algorithm>
      #include<iostream>
      #include<string>
      #include<cstring>
      #include<cmath>
      //999911658=2*3*4679*35617
      #define LL long long
      #define mod 999911659
      using namespace std;
      LL N,G,e;
      LL x[4];
      LL pre[4][40000];
      LL ni[4][40000];
      LL zs[4]={2,3,4679,35617};
      LL gcd(LL a,LL b,LL &x,LL &y)//求逆元
      {
          if(b==0) {x=1;y=0;}
          else     {gcd(b,a%b,y,x); y-=(a/b)*x;}
      }
      LL lucas(LL p,LL q,LL o)//卢卡斯定理
      {
          LL sum=1;
          while(p && q)
          {
              LL x=p%zs[o],y=q%zs[o];
              if(y>x) return 0;
              sum=(sum*(pre[o][x]*(ni[o][x-y]*ni[o][y])%zs[o])%zs[o])%zs[o];
              p/=zs[o];
              q/=zs[o];
          }
          return sum;
      }
      int main()
      {
          scanf("%lld%lld",&N,&G);
          if(G%mod==0) {printf("0\n");return 0;}
          for(int o=0;o<4;o++)//预处理
          {
              pre[o][0]=1;ni[o][0]=1; 
              for(int i=1;i<=zs[o];i++)
              pre[o][i]=(pre[o][i-1]*i)%zs[o];
              ni[o][zs[o]-1]=zs[o]-1;
              for(int i=zs[o]-2;i>=1;i--)
              ni[o][i]=(ni[o][i+1]*(i+1))%zs[o];
              for(LL i=1;i<=sqrt(N);i++)//统计组合数
              if(N%i==0)
              {
                  x[o]=(x[o]+lucas(N,i,o))%zs[o];
                  if(i*i<N) x[o]=(x[o]+lucas(N,N/i,o))%zs[o];
              }
          };
          for(int i=0;i<4;i++)//中国剩余定理
          {
              LL o,p;
              LL M=(mod-1)/zs[i];
              gcd(M,zs[i],o,p);
              e=(e+x[i]*o*M)%(mod-1);
          }
          while(e<=0) e+=mod-1;
          LL ans=1,a=G;
          while(e)
          {
              if(e&1) ans=(ans*a)%mod;
              a=(a*a)%mod;
              e>>=1;
          }
          printf("%lld\n",ans);
          return 0;
      }
      
      • 1

      信息

      ID
      124
      时间
      1000ms
      内存
      128MiB
      难度
      1
      标签
      递交数
      29
      已通过
      27
      上传者