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 $y \text{ XOR } x$.

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 $10^9 + 7$.

2 3

3

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

10 100

604

1 1000000000000000000

68038601

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