Farmer John commanded his cows to search for different sets of numbers that sum to a given number. The cows use only numbers that are an integer power of 2. Here are the possible sets of numbers that sum to 7:

1) 1+1+1+1+1+1+1 
2) 1+1+1+1+1+2 
3) 1+1+1+2+2 
4) 1+1+1+4 
5) 1+2+2+2 
6) 1+2+4

Help FJ count all possible representations for a given integer N (1 <= N <= 1,000,000).

A single line with a single integer, N.

The number of ways to represent N as the indicated sum. Due to the potential huge size of this number, print only last 9 digits (in base 10 representation).

7

6

#include<iostream>

#include<algorithm>

using namespace std;

int dp[];

int mod=1e9;

int main(){

    int n;

    cin>>n;

    dp[]=;

    for(int i=;i<=n;i++){

        if(i%==){

            dp[i]=dp[i-];

        }

        else{

            dp[i]=(dp[i-]+dp[i>>])%mod;

        }

    }

    cout<<dp[n]<<endl;

    return ;

}