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.

Examples

Input

2 3

Output

3

Input

10 100

Output

604

Input

1 1000000000000000000

Output

68038601

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