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 (7.3.0) (judge verdict: Accepted)

L, R = map(int, input().split())
dp = [[[[0]*2 for _ in range(2)] for _ in range(2)] for _ in range(65)]
dp[0][0][0][0] = 1
MOD = 10**9+7

for i in range(64):
    Li = (L>>(63-i))&1
    Ri = (R>>(63-i))&1
    
    for j in range(2):
        for k in range(2):
            for l in range(2):
                for x in (range(2) if j else range(Li, 2)):
                    for y in range(2 if k else Ri+1):
                        if x==1 and y==0:
                            continue
                        
                        if l==0 and x==0 and y==1:
                            continue
                        
                        dp[i+1][j|(x>Li)][k|(y<Ri)][l|(x==1 and y==1)] += dp[i][j][k][l]
                        dp[i+1][j|(x>Li)][k|(y<Ri)][l|(x==1 and y==1)] %= MOD

ans = 0

for i in range(2):
    for j in range(2):
        for k in range(2):
            ans += dp[-1][i][j][k]
            ans %= MOD

print(ans)