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Contest: Task: Related: TaskE TaskG

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

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

Sample Input 2

10 100

Sample Output 2

Sample Input 3

1 1000000000000000000

Sample Output 3

68038601

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