【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 = 1000005;
const int MOD = 1e6 + 3;

s64 n, k;
s64 num = 0;
s64 Fz = 1, Fm = 1;

int get() 
{ 
        int res;char c; 
        while( (c=getchar())<48 || c>57 );
        res=c-48;  
        while( (c=getchar())>=48 && c<=57 )
        res=res*10+c-48; 
        return res; 
}

s64 Quickpow(s64 a, s64 b)
{
        s64 res = 1;
        while(b)
        {
            if(b & 1) res = res * a % MOD;
            a = a * a % MOD;
            b >>= 1;
        }
        return res;
}

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

        num = 1;
        while((1LL << num) < k) num++;
        if(num > n) {printf("1 1"); return 0;}

        num = 0;
        for(s64 i = k - 1; i >= 1; i >>= 1)
            num += (i >> 1);

        s64 a = Quickpow(2, n);

        Fz = 1;
        for(int i = 1; i < k; i++)
        {
            Fz = (s64)Fz * (a - i + MOD) % MOD;
            if(Fz == 0) break;
        }
        Fm = Quickpow(a, k - 1);

        int inv = Quickpow(Quickpow(2, num), MOD - 2);

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


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