Poj1845

Sumdiv

Time Limit: 1000MS Memory Limit: 30000KTotal Submissions: 17258 Accepted: 4335

Description

Consider two natural numbers A and B. Let S be the sum of all natural divisors of A^B. Determine S modulo 9901 (the rest of the division of S by 9901).

Input

The only line contains the two natural numbers A and B, (0 <= A,B <= 50000000)separated by blanks.

Output

The only line of the output will contain S modulo 9901.

Sample Input

2 3

Sample Output

15

Hint

2^3 = 8.
The natural divisors of 8 are: 1,2,4,8. Their sum is 15.
15 modulo 9901 is 15 (that should be output).

 

 

#include<iostream>#include<cmath>//#define LL long longtypedef long long LL;using namespace std;struct mc{LL prime;LL count;}s[10000];int prime(LL x){      if(x==2){return 1;}      if(x<=1 || x%2==0){return 0;}      LL j=3;      while(j<=(LL)sqrt(double(x))){               if(x%j==0){return 0;}               j=j+2;              }      return 1;    }    LL modular(LL a, LL r, LL m){            LL d=1,t=a;            while(r>0){                if(r%2==1){d=d*t%m;}                 r=r/2;                 t=t*t%m;                    }          return d;                 }int fun(LL a){int j=0;     for(int i=2;i*i<=a;){     if(a%i==0){        j++;        s[j].prime=i;        s[j].count=0;        }while(a%i==0){      s[j].count++;      a=a/i;}if(i==2){i++;}else{i=i+2;}     }     if(a!=1){     j++;     s[j].prime=a;     s[j].count=1;     }     return j;}                            LL gui(LL p,LL n){if(n==0){return 1;}    if(n%2==0){return (  (1+modular(p,n/2+1,9901))*(gui(p,n/2-1)) + modular(p,n/2,9901))%9901;}    if(n%2==1){return (  (1+modular(p,n/2+1,9901))*(gui(p,n/2)) )%9901;}}int main(){    LL a,b,mi,len,ans=1;    scanf("%I64d%I64d",&a,&b);    if(a==0){printf("0\n");return 0;}    mi=modular(a,b,9901);    //printf("%I64d",mi);    len=fun(a);    /*for(int i=1;i<=len;i++){    printf("%I64d %I64d\n",s[i].prime,s[i].count);    }*/    for(int i=1;i<=len;i++){      ans=ans*gui(s[i].prime,s[i].count*b)%9901;    }    printf("%I64d",ans);system("pause");return 0;    }