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())
  mod = 10**9 + 7
  l = "{:060b}".format(L)
  r = "{:060b}".format(R)
  
  memo = [[[[-1] * 2 for i in range(2)] for j in range(2)] for k in range(60)]
  
  
  def f(pos, flagL, flagR, flagM):
      if pos == 60:
          return 1
      if memo[pos][flagL][flagR][flagM] != -1:
          return memo[pos][flagL][flagR][flagM]
      ret = 0
      # (0, 0)
      if flagL or l[pos] == "0":
          ret += f(pos + 1, flagL, 1 if r[pos] == "1" else flagR, flagM)
      # (0, 1)
      if flagM and (flagL or l[pos] == "0") and (flagR or r[pos] == "1"):
          ret += f(pos + 1, flagL, flagR, flagM)
      # (1, 1)
      if flagR or r[pos] == "1":
          ret += f(pos + 1, 1 if l[pos] == "0" else flagL, flagR, 1)
      memo[pos][flagL][flagR][flagM] = ret % mod
      return ret % mod
  
  
  print(f(0, 0, 0, 0) % mod)
  
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."}]