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: import sys
  
  sys.setrecursionlimit(2147483647)
  INF = float("inf")
  MOD = 10**9 + 7
  input = lambda: sys.stdin.readline().rstrip()
  from itertools import product
  
  
  def resolve():
      L, R = map(int, input().split())
      L = map(int, bin(L)[2:].zfill(60))
      R = map(int, bin(R)[2:].zfill(60))
  
      dp = [[[0] * 2 for _ in range(2)] for _ in range(2)]
      dp[0][0][0] = 1  # dp[msb][mt][lt]
  
      for l, r in zip(L, R):
          ndp = [[[0] * 2 for _ in range(2)] for _ in range(2)]
          for msb, mt, lt, x, y in product(range(2), repeat=5):
              if (not msb) and (x != y):
                  continue
              if (not mt) and l > x:
                  continue
              if (not lt) and y > r:
                  continue
              if x > y:
                  continue
              ndp[max(msb, x * y == 1)][max(mt, l < x)][max(lt, y < r)] += dp[msb][mt][lt]
              ndp[max(msb, x * y == 1)][max(mt, l < x)][max(lt, y < r)] %= MOD
          dp = ndp
  
      print(sum(dp[msb][mt][lt] for msb, mt, lt in product(range(2), repeat=3)) % MOD)
  
  
  resolve()
  
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."}]