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.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
    static final int MODULUS = 1_000_000_007;

    static Map<Long, Integer> cache = new HashMap<>();

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        long N = sc.nextLong();

        System.out.println(solve(N));

        sc.close();
    }

    // http://oeis.org/A007729
    static int solve(long N) {
        if (N <= 1) {
            return (int) N + 1;
        }

        if (cache.containsKey(N)) {
            return cache.get(N);
        }

        int result;
        if (N % 2 == 0) {
            result = addMod(multiplyMod(solve(N / 2 - 1), 2), solve(N / 2));
        } else {
            result = addMod(multiplyMod(solve(N / 2), 2), solve(N / 2 - 1));
        }
        cache.put(N, result);

        return result;
    }

    static int addMod(int x, int y) {
        return (x + y) % MODULUS;
    }

    static int multiplyMod(int x, int y) {
        return (int) ((long) x * y % MODULUS);
    }
}