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Consider the following function $f(x)$, which takes a single positive integer as argument, and returns an integer.

It can be shown that for any positive integer $X$, this function terminates. Given an interval $[L, R]$, compute the sum

$S = f (L) + f (L + 1) + · · · + f (R − 1) + f (R)$

Input

The first and only line of input contains two integers $L$ and $R$ $(1 \leq L \leq R \leq 10^{18})$.

Output

Output the result $S$ modulo the prime $10^9 + 7$.

Sample test(s)