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: MOD = 10**9 + 7
  
  L, R = [int(item) for item in input().split()]
  L_blen = L.bit_length()
  R_blen = R.bit_length()
  
  # dp[y loose/tight][x loose/tight][index]
  dp = [[[0] * (R_blen + 1) for _ in range(2)] for _ in range(2)]
  
  for i in range(R_blen + 1):
      L_bit = L & (1 << R_blen - i)
      R_bit = R & (1 << R_blen - i)
  
      # Form R's MSB to L's LSB can be the initial bit
      curbit_idx = R_blen - i + 1
      if curbit_idx <= R_blen and curbit_idx >= L_blen:
          dp[R_blen == curbit_idx][L_blen == curbit_idx][i] += 1
  
      # R=0, L=0
      if not R_bit and not L_bit:
          # y=1, x=1
          dp[0][0][i] += dp[0][0][i - 1]
          dp[0][0][i] += dp[0][1][i - 1]
          # y=0, x=0
          dp[1][1][i] += dp[1][1][i - 1]
          dp[1][0][i] += dp[1][0][i - 1]
          dp[0][0][i] += dp[0][0][i - 1]
          dp[0][1][i] += dp[0][1][i - 1]
          # y=1, x=0
          dp[0][1][i] += dp[0][1][i - 1]
          dp[0][0][i] += dp[0][0][i - 1]
  
      # R=1, L=0
      if R_bit and not L_bit:
          # y=1, x=1
          dp[0][0][i] += dp[0][0][i - 1]
          dp[1][0][i] += dp[1][0][i - 1]
          dp[0][0][i] += dp[0][1][i - 1]
          dp[1][0][i] += dp[1][1][i - 1]
          # y=0, x=0
          dp[0][0][i] += dp[0][0][i - 1]
          dp[0][0][i] += dp[1][0][i - 1]
          dp[0][1][i] += dp[0][1][i - 1]
          dp[0][1][i] += dp[1][1][i - 1]
          # y=1, x=0
          dp[0][0][i] += dp[0][0][i - 1]
          dp[1][0][i] += dp[1][0][i - 1]
          dp[0][1][i] += dp[0][1][i - 1]
          dp[1][1][i] += dp[1][1][i - 1]
  
      # R=0, L=1
      if not R_bit and L_bit:
          # y=1, x=1
          dp[0][0][i] += dp[0][0][i - 1]
          dp[0][1][i] += dp[0][1][i - 1]
          # y=0, x=0
          dp[0][0][i] += dp[0][0][i - 1]
          dp[1][0][i] += dp[1][0][i - 1]
          # y=1, x=0
          dp[0][0][i] += dp[0][0][i - 1]
  
      # R=1, L=1
      if R_bit and L_bit:
          # y=1, x=1
          dp[0][0][i] += dp[0][0][i - 1]
          dp[1][0][i] += dp[1][0][i - 1]
          dp[0][1][i] += dp[0][1][i - 1]
          dp[1][1][i] += dp[1][1][i - 1]
          # y=0, x=0
          dp[0][0][i] += dp[1][0][i - 1]
          dp[0][0][i] += dp[0][0][i - 1]
          # y=1, x=0
          dp[1][0][i] += dp[1][0][i - 1]
          dp[0][0][i] += dp[0][0][i - 1]
  
      # Take MOD
      for i in range(2):
          for j in range(2):
              dp[i][j][i] %= MOD
  
  ans = 0
  for i in range(2):
      for j in range(2):
          ans += dp[i][j][-1]
          ans %= MOD
  print(ans)
  
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."}]