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 = len(bin(r)) - 2
  L = format(l, "b").zfill(M)
  R = format(r, "b")
  mod = 10**9 + 7
  dp = [[0 for l in range(70)] for i in range(5)]
  if L[0] == "1":
      dp[2][0] = 1
  else:
      dp[3][0] = 1
      dp[0][0] = 1
  for i in range(1, M):
      if L[i] == "1" and R[i] == "1":
          dp[1][i] = (dp[0][i - 1] + dp[1][i - 1]) % mod
          dp[2][i] = (dp[2][i - 1]) % mod
          dp[3][i] = (2 * dp[3][i - 1]) % mod
          dp[4][i] = (dp[3][i - 1] + 3 * dp[4][i - 1]) % mod
      elif L[i] == "1" and R[i] == "0":
          dp[1][i] = dp[1][i - 1] + dp[0][i - 1]
          dp[3][i] = dp[3][i - 1]
          dp[4][i] = (dp[4][i - 1] * 3) % mod
      elif L[i] == "0" and R[i] == "1":
          dp[0][i] = dp[0][i - 1]
          dp[1][i] = (2 * dp[1][i - 1] + dp[2][i - 1]) % mod
          dp[2][i] = dp[2][i - 1]
          dp[3][i] = (dp[2][i - 1] + dp[3][i - 1] * 2) % mod
          dp[4][i] = (dp[0][i - 1] + dp[1][i - 1] + dp[3][i - 1] + dp[4][i - 1] * 3) % mod
      else:
          dp[0][i] = dp[0][i - 1]
          dp[1][i] = (dp[1][i - 1] * 2) % mod
          dp[2][i] = dp[2][i - 1]
          dp[3][i] = (dp[3][i - 1]) % mod
          dp[4][i] = (dp[0][i - 1] + dp[1][i - 1] + dp[4][i - 1] * 3) % mod
  ans = 0
  for i in range(5):
      ans += dp[i][M - 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."}]