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).
Input
A single line with a single integer, N.
Output
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).
Sample Input
7
Sample Output
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 ;
}