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
  
  
  def solve(N):
      n = N.bit_length()
      dp = [[0 for i in range(4)] for j in range(n)]
      dp[0][0] = 1 + (N % 2 == 1)
      dp[0][1] = 1 + 2 * (N % 2 == 1)
      dp[0][2] = 2
      dp[0][3] = 3
      for i in range(1, n):
          for j in range(4):
              if j == 0:
                  if N >> i & 1 == 1:
                      dp[i][j] = dp[i - 1][2] + dp[i - 1][1]
                  else:
                      dp[i][j] = dp[i - 1][0]
              elif j == 1:
                  if N >> i & 1 == 1:
                      dp[i][j] = dp[i - 1][3] + 2 * dp[i - 1][1]
                  else:
                      dp[i][j] = dp[i - 1][1]
              elif j == 2:
                  dp[i][j] = dp[i - 1][2] + dp[i - 1][3]
              else:
                  dp[i][j] = 3 * dp[i - 1][3]
  
      return dp[-1][0] - 1
  
  
  def extra(N):
      if N == 0:
          return 0
      n = N.bit_length()
      dp = [[0 for i in range(4)] for j in range(n)]
      dp[0][0] = 1 + (N % 2 == 1)
      dp[0][1] = 2 + (N % 2 == 1)
      dp[0][2] = 2
      dp[0][3] = 3
      for i in range(1, n):
          for j in range(4):
              if j == 0:
                  if N >> i & 1 == 1:
                      dp[i][j] = dp[i - 1][2] + dp[i - 1][1]
                  else:
                      dp[i][j] = dp[i - 1][0]
              elif j == 1:
                  if N >> i & 1 == 1:
                      dp[i][j] = 2 * dp[i - 1][3] + dp[i - 1][1]
                  else:
                      dp[i][j] = 2 * dp[i - 1][1]
              elif j == 2:
                  dp[i][j] = dp[i - 1][2] + dp[i - 1][3]
              else:
                  dp[i][j] = 3 * dp[i - 1][3]
  
      return dp[-1][0] - 1
  
  
  L, R = map(int, input().split())
  print((solve(R) - extra(L - 1)) % 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."}]