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
  
  DP_ini = [[[0 for i in range(2)] for j in range(2)] for k in range(64)]
  
  import copy
  
  ANS = 0
  
  for begin in range(64):
      DP = copy.deepcopy(DP_ini)
  
      if L < (1 << (begin + 1)) and (1 << begin) <= R:
  
          if not (1 << begin <= L < 1 << (begin + 1)) and not (
              1 << begin <= R < 1 << (begin + 1)
          ):
              DP[begin][0][0] = 1
  
          elif 1 << begin <= L < 1 << (begin + 1) and not (
              1 << begin <= R < 1 << (begin + 1)
          ):
              DP[begin][1][0] = 1
  
          elif not (1 << begin <= L < 1 << (begin + 1)) and 1 << begin <= R < 1 << (
              begin + 1
          ):
              DP[begin][0][1] = 1
  
          else:
              DP[begin][1][1] = 1
  
      for keta in range(begin - 1, -1, -1):
  
          if L & (1 << keta) == 0 and R & (1 << keta) == 0:
              DP[keta][0][0] = (
                  DP[keta][0][0]
                  + DP[keta + 1][0][0] * 3
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 1
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][0][1] = (
                  DP[keta][0][1]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 1
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][1][0] = (
                  DP[keta][1][0]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 2
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][1][1] = (
                  DP[keta][1][1]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 1
              )
  
          elif L & (1 << keta) != 0 and R & (1 << keta) == 0:
              DP[keta][0][0] = (
                  DP[keta][0][0]
                  + DP[keta + 1][0][0] * 3
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][0][1] = (
                  DP[keta][0][1]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 1
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][1][0] = (
                  DP[keta][1][0]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 1
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][1][1] = (
                  DP[keta][1][1]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 0
              )
  
          elif L & (1 << keta) == 0 and R & (1 << keta) != 0:
              DP[keta][0][0] = (
                  DP[keta][0][0]
                  + DP[keta + 1][0][0] * 3
                  + DP[keta + 1][0][1] * 1
                  + DP[keta + 1][1][0] * 1
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][0][1] = (
                  DP[keta][0][1]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 2
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 1
              )
              DP[keta][1][0] = (
                  DP[keta][1][0]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 2
                  + DP[keta + 1][1][1] * 1
              )
              DP[keta][1][1] = (
                  DP[keta][1][1]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 1
              )
          else:
              DP[keta][0][0] = (
                  DP[keta][0][0]
                  + DP[keta + 1][0][0] * 3
                  + DP[keta + 1][0][1] * 1
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][0][1] = (
                  DP[keta][0][1]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 2
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][1][0] = (
                  DP[keta][1][0]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 1
                  + DP[keta + 1][1][1] * 0
              )
              DP[keta][1][1] = (
                  DP[keta][1][1]
                  + DP[keta + 1][0][0] * 0
                  + DP[keta + 1][0][1] * 0
                  + DP[keta + 1][1][0] * 0
                  + DP[keta + 1][1][1] * 1
              )
  
      # print(begin,DP[0])
      ANS += sum(DP[0][0]) + sum(DP[0][1])
  
  print(ANS % 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."}]