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: def count(lb, rb, MOD):
      assert lb[0] == "1"
      assert rb[0] == "1"
      assert len(lb) == len(rb)
      i = 0
      for i, (lc, rc) in enumerate(zip(lb, rb)):
          if lc != rc:
              break
      else:
          return 1
      dp = [1, 0, 1]
      for lc, rc in zip(lb[i + 1 :], rb[i + 1 :]):
          ndp = [0, 0, 0]
          if rc == "0":
              ndp[0] += dp[0]
          else:
              ndp[0] += dp[0] * 2
              ndp[1] += dp[0]
              if lc == "0":
                  ndp[0] += 1
                  ndp[2] += 1
          if lc == "0":
              ndp[1] += dp[2]
              ndp[2] += dp[2] * 2
          else:
              ndp[2] += dp[2]
          ndp[1] += dp[1] * 3
          ndp[0] %= MOD
          ndp[1] %= MOD
          dp = ndp
      return sum(dp) + 1
  
  
  l, r = map(int, input().split())
  lb = bin(l)[2:]
  rb = bin(r)[2:]
  ld = len(lb)
  rd = len(rb)
  ans = 0
  MOD = 10**9 + 7
  for d in range(ld, rd + 1):
      tlb = lb if d == ld else "1" + "0" * (d - 1)
      trb = rb if d == rd else "1" * d
      ans = (ans + count(tlb, trb, MOD)) % 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."}]