【Codeforces711E】ZS and The Birthday Paradox [数论]

ZS and The Birthday Paradox

Time Limit: 20 Sec  Memory Limit: 512 MB

Description

　　

Input

　　

Output

　　

Sample Input

　　4 3

Sample Output

　　23 128

HINT

　　

Solution

　　

Code

 #include<iostream>
 #include<string>
 #include<algorithm>
 #include<cstdio>
 #include<cstring>
 #include<cstdlib>
 #include<cmath>
 #include<vector>
 using namespace std;
 typedef long long s64;

 const int ONE = ;
 const int MOD = 1e6 + ;

 s64 n, k;
 s64 num = ;
 s64 Fz = , Fm = ;

 int get()
 {
         int res;char c;
         while( (c=getchar())< || c> );
         res=c-;
         while( (c=getchar())>= && c<= )
         res=res*+c-;
         return res;
 }

 s64 Quickpow(s64 a, s64 b)
 {
         s64 res = ;
         while(b)
         {
             if(b & ) res = res * a % MOD;
             a = a * a % MOD;
             b >>= ;
         }
         return res;
 }

 int main()
 {
         cin>>n>>k;

         num = ;
         while((1LL << num) < k) num++;
         if(num > n) {printf("1 1"); return ;}

         num = ;
         for(s64 i = k - ; i >= ; i >>= )
             num += (i >> );

         s64 a = Quickpow(, n);

         Fz = ;
         for(int i = ; i < k; i++)
         {
             Fz = (s64)Fz * (a - i + MOD) % MOD;
             if(Fz == ) break;
         }
         Fm = Quickpow(a, k - );

         int inv = Quickpow(Quickpow(, num), MOD - );

         Fz = (s64)Fz * inv % MOD, Fm = (s64)Fm * inv % MOD;
         Fz = (Fm - Fz + MOD) % MOD;

         cout<<Fz<<" "<<Fm<<endl;
 }