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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
	
	static Map<Long, Long> check = new HashMap<Long, Long>();
	
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String buf;
		String[] input;
		long N;
		
		N = Long.parseLong(br.readLine());
		
		System.out.println(solve(N));
	}
	
	static long solve(long n) {
		long a, b;
		
		if(n == 0) return 1;
		if(n == 1) return 2;
		
		if(check.containsKey(n/2)) {
			a = check.get(n/2);
		} else {
			a = solve(n/2) % 1000000007;
			check.put(n/2, a);
		}
		
		if(check.containsKey(n/2-1)) {
			b = check.get(n/2-1);
		} else {
			b = solve(n/2-1) % 1000000007;
			check.put(n/2-1, b);
		}
		
		if(n % 2 == 1) {
			return (2*a + b) % 1000000007;
		} else {
			return (2*b + a) % 1000000007;
		}
	}
}