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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
class Solve{
    public Solve(){}
    StringBuilder sb;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        long N = long.Parse(Console.ReadLine());
        long M = N;
        long count = 0;
        long[,] dp = new long[63,3];
        dp[0,0] = 1;
        int i;
        for(i=1;i<63;i++){
            if(M <= 3){
                break;
            }
            M /= 2;
            if((N & (1 << (i - 1))) != 0){
                dp[i,0] = (2*dp[i-1,0] + dp[i-1,1]) % Define.mod;
                dp[i,1] = (dp[i-1,0] + 2*dp[i-1,1] + 2*dp[i-1,2]) % Define.mod;
                dp[i,2] = dp[i-1,2]; 
            }
            else{
                dp[i,0] = dp[i-1,0];
                dp[i,1] = (2*dp[i-1,0] + 2*dp[i-1,1] + dp[i-1,2]) % Define.mod;
                dp[i,2] = (dp[i-1,1] + 2*dp[i-1,2]) % Define.mod;
            }
        }
        if(M == 1){
            count = 2;
        }
        else if(M == 2){
            count = (4*dp[i-1,0] + 2*dp[i-1,1] + dp[i-1,2]) % Define.mod;
        }
        else{
            count = (5*dp[i-1,0] + 4*dp[i-1,1] + 2*dp[i-1,2]) % Define.mod;
        }
        sb.Append(count+"\n");
    }
}
public static class Define{
    public const long mod = 1000000007;
}