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 = ConsoleReader.LongArray();
      var l = input[0];
      var r = input[1];
      var k = (long)Math.Pow(10, 9) + 7;

      var count = 0L;
      for (var y = l; y <= r; y++)
      {
        var ys = Convert.ToString(y, 2);
        var p = 0;
        foreach (var b in ys)
        {
          if (b == '1')
          {
            p++;
          }
        }
        count += (long)Math.Pow(2, p - 1);
      }
      return count % k;
    }
  }

  internal static class ConsoleReader
  {
    public static string String()
    {
      return Console.ReadLine();
    }

    public static int Int()
    {
      return int.Parse(Console.ReadLine());
    }

    public static int[] IntArray()
    {
      return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
    }

    public static long Long()
    {
      return long.Parse(Console.ReadLine());
    }

    public static long[] LongArray()
    {
      return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
    }

    public static double Double()
    {
      return double.Parse(Console.ReadLine());
    }

    public static double[] DoubleArray()
    {
      return Console.ReadLine().Split(' ').Select(double.Parse).ToArray();
    }
  }
}