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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;

class Program
{
    static long n;
    static long mod = (long)1e9 + 7;
    static SortedList<long, long> sl = new SortedList<long, long>
        {
            { 0, 1 },
            { 1, 1 }
        };

    static void Main()
    {
        n = long.Parse(Console.ReadLine());
        Console.WriteLine(Ans(n));
    }

    static long h(long n)
    {
        if (sl.ContainsKey(n)) return sl[n];
        long t;
        if (n % 2 == 1)
        {
            t = h(n / 2);
            sl.Add(n, t);
            return t;
        }
        long t1 = h(n / 2);
        long t2 = h(n / 2 - 1);
        t = (t1 + t2) % mod;
        sl.Add(n, t);
        return t;
    }

    static long Ans(long n)
    {
        if (n == 0) return 1;
        if (n == 1) return 2;
        long m = n / 2;
        long s = Ans(m - 1);
        long hm = h(m);
        if (n % 2 == 0)
            return (3 * s % mod + hm) % mod;
        return (3 * s % mod + 2 * hm % mod) % mod;
    }
}