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: Time Limit Exceeded)

L,R=map(int,input().split())
mod=10**9+7

def calc(keta,l,r):

    if keta==-1:
        if l>=L and r<=R:
            return 1
        else:
            return 0
    
    ANS=0
    
    if l==r==0:
        if (1<<keta)<=R:
            ANS=ANS+calc(keta-1,1<<keta,1<<keta)
            ANS%=mod

        ANS=ANS+calc(keta-1,0,0)
        ANS%=mod

    else:
        if l>=L and (1<<(keta+1))+r<=R:
            ANS=ANS+pow(3,keta+1,mod)
            ANS%=mod

        else:
            if r+(1<<keta)<=R:
                ANS+=calc(keta-1,l+(1<<keta),r+(1<<keta))
                ANS%=mod

            if r+(1<<keta)<=R and l+(1<<keta)>L:
                ANS+=calc(keta-1,l,r+(1<<keta))
                ANS%=mod

            if l+(1<<keta)>L:
                ANS+=calc(keta-1,l,r)
                ANS%=mod

    return ANS

print(calc(72,0,0))