Problem:
Score : 600 points

Problem Statement

You are given a positive integer N.
Find the number of the pairs of integers u and v (0≦u,v≦N) such that there exist two non-negative integers a and b satisfying a xor b=u and a+b=v.
Here, xor denotes the bitwise exclusive OR.
Since it can be extremely large, compute the answer modulo 10^9+7.

Constraints

1≦N≦10^{18}

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the possible pairs of integers u and v, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

5

The five possible pairs of u and v are:

u=0,v=0 (Let a=0,b=0, then 0 xor 0=0, 0+0=0.)

u=0,v=2 (Let a=1,b=1, then 1 xor 1=0, 1+1=2.）

u=1,v=1 (Let a=1,b=0, then 1 xor 0=1, 1+0=1.）

u=2,v=2 (Let a=2,b=0, then 2 xor 0=2, 2+0=2.）

u=3,v=3 (Let a=3,b=0, then 3 xor 0=3, 3+0=3.）

Sample Input 2

1422

Sample Output 2

52277

Sample Input 3

1000000000000000000

Sample Output 3

787014179

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define LL long long
#define MOD (1000000007)
using namespace std;

LL n;
map<pair<LL,LL>,int>f;

int DFS(LL u,LL v)
{
	if (!v) return 1;
	if (f[make_pair(u,v)]) return f[make_pair(u,v)];
	int ans=0;
	(ans+=DFS(u>>1,v>>1))%=MOD;
	(ans+=DFS((u-1)>>1,(v-1)>>1))%=MOD;
	if (v>=2) (ans+=DFS(u>>1,(v-2)>>1))%=MOD;
	return f[make_pair(u,v)]=ans;
}

int main()
{
	cin>>n;
	cout<<DFS(n,n)<<endl;
}