Problem:
Score : 600 points

Problem Statement

Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x.

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

1 \leq L \leq R \leq 10^{18}

Input

Input is given from Standard Input in the following format:

L R

Output

Print the number of pairs of integers (x, y) (L \leq x \leq y \leq R) satisfying the condition, modulo 10^9 + 7.

Sample Input 1

2 3

Sample Output 1

3

Three pairs satisfy the condition: (2, 2), (2, 3), and (3, 3).

Sample Input 2

10 100

Sample Output 2

604

Sample Input 3

1 1000000000000000000

Sample Output 3

68038601

Be sure to compute the number modulo 10^9 + 7.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

namespace F
{
  class Program
  {
    static void Main(string[] args)
    {
      Console.WriteLine(Run(args));
    }
    private static double Run(string[] args)
    {
      var input = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
      var l = input[0];
      var r = input[1];
      var k = (long)Math.Pow(10, 9) + 7;

      var count = 0L;
      var ls = Convert.ToString(l, 2);
      var rs = Convert.ToString(r, 2);
      if (rs.Length - ls.Length >= 2)
      {
        for (int i = ls.Length + 1; i < rs.Length; i++)
        {
          count += (long)Math.Pow(3, i - 1);
        }

        var lmaxs = string.Join(string.Empty, Enumerable.Repeat('1', ls.Length));
        var lmax = Convert.ToInt64(lmaxs, 2);
        for (var y = l; y <= lmax; y++)
        {
          for (var x = l; x <= y; x++)
          {
            var rem = y % x;
            var xor = y ^ x;
            if (rem.Equals(xor))
            {
              count++;
            }
          }
        }

        var rmins = string.Join(string.Empty, Enumerable.Concat(Enumerable.Repeat('1', 1), Enumerable.Repeat('0', rs.Length - 1)));
        var rmin = Convert.ToInt64(rmins, 2);
        for (var y = rmin; y <= r; y++)
        {
          for (var x = rmin; x <= y; x++)
          {
            var rem = y % x;
            var xor = y ^ x;
            if (rem.Equals(xor))
            {
              count++;
            }
          }
        }
      }
      else
      {
        for (var y = l; y <= r; y++)
        {
          for (var x = l; x <= y; x++)
          {
            var rem = y % x;
            var xor = y ^ x;
            if (rem.Equals(xor))
            {
              count++;
            }
          }
        }
      }
      return count % k;
    }
  }
}