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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Tasks
{
    public class D
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var N = long.Parse(Console.ReadLine());
            var p = (int)1e9 + 7;
            var dp = new int[61][].Select(x => x = new int[3]).ToArray();
            dp[60][0] = 1;
            for (var i = 59; i >= 0; i--)
            {
                for (var j = 0; j <= 2; j++)
                {
                    var u = (N >> i) & 1;
                    if (j * 2 - 2 + u >= 0)
                    {
                        var j11 = Math.Min(2, j * 2 - 2 + u);
                        dp[i][j11] += dp[i + 1][j];
                        dp[i][j11] %= p;
                    }

                    if (j * 2 - 1 + u >= 0)
                    {
                        var j01 = Math.Min(2, j * 2 - 1 + u);
                        dp[i][j01] += dp[i + 1][j];
                        dp[i][j01] %= p;
                    }

                    var j00 = Math.Min(2, j * 2 + u);
                    dp[i][j00] += dp[i + 1][j];
                    dp[i][j00] %= p;
                }
            }

            var answer = 0L;
            for (var i = 0; i <= 2; i++)
            {
                answer += dp[0][i];
                answer %= p;
            }
            Console.WriteLine(answer);
        }
    }
}