Problem:
Score : 600 points

Problem 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.)

Constraints

1 \leq L \leq R \leq 10^{18}

Input

Input is given from Standard Input in the following format:

L R

Output

Print the number of pairs of integers (x, y) (L \leq x \leq y \leq R) satisfying the condition, modulo 10^9 + 7.

Sample Input 1

2 3

Sample Output 1

3

Three pairs satisfy the condition: (2, 2), (2, 3), and (3, 3).

Sample Input 2

10 100

Sample Output 2

604

Sample Input 3

1 1000000000000000000

Sample Output 3

68038601

Be sure to compute the number modulo 10^9 + 7.

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

def i1():
 return int(input())
def i2():
 return [int(i) for i in input().split()]
[l,r]=i2()
z=10**9+7
dp=[[[[0 for l in range(2)]for k in range(2)]for j in range(2)]for i in range(61)]
dp[60][0][0][0]=1
for n in range(60)[::-1]:
 lb=l>>n&1
 rb=r>>n&1
 for x in range(2):
  for y in range(2):
   for i in range(2):
    for j in range(2):
     for k in range(2):
      ni=i+0
      nj=j+0
      nk=k+0
      if x>y:
         continue
      if k==0 and x!=y:
         continue
      if x&y:
         nk=1
      if i==0 and x<lb:
         continue
      if  x>lb:
         ni=1
      if j==0 and y>rb:
         continue
      if y<rb:
         nj=1
      dp[n][ni][nj][nk]+=dp[n+1][i][j][k]
      dp[n][ni][nj][nk]%=z
print((dp[0][1][1][1]+dp[0][0][1][1]+dp[0][1][0][1]+dp[0][0][0][1])%z)