output_description: Print the number of pairs of integers (x, y) (L \leq x \leq y \leq R)
  satisfying the condition, modulo 10^9 + 7.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      L R
attempt: l, r = map(int, input().split())
  m = 10**9 + 7
  f = [1]
  for i in range(100):
      f += [f[-1] * (i + 1) % m]
  
  
  def comb(aa, bb, mm):
      return f[aa] * pow(f[bb], mm - 2, mm) * pow(f[aa - bb], mm - 2, mm) % mm
  
  
  s = bin(l)[2:]
  n = len(s)
  a = 0
  b = 0
  for i in range(1, n):
      if s[i] == "0":
          c = 2**b % m
          for j in range(n - i):
              a += comb(n - i, j, m) * c
              a %= m
              c *= 2
          b += 1
  s = bin(r)[2:]
  n = len(s)
  b = 0
  for i in range(1, n):
      if s[i] == "1":
          c = 2 ** (n - b - 1) % m
          for j in range(n - i):
              a += comb(n - i, j, m) * c
              a %= m
              c //= 2
          b += 1
  for i in range(len(bin(l)[2:]) + 1, len(bin(r)[2:]) + 1):
      b = 1
      for j in range(i):
          a += comb(i, j, m) * b
          a %= m
          b *= 2
  print(a)
  
problem_description: 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.)
samples: [{"input": "2 3", "output": "3\n    \n\nThree pairs satisfy the condition: (2, 2), (2, 3), and (3, 3).\n\n* * *"}, {"input": "10 100", "output": "604\n    \n\n* * *"}, {"input": "1 1000000000000000000", "output": "68038601\n    \n\nBe sure to compute the number modulo 10^9 + 7."}]