You are given two non-negative integers L and R represented as decimal strings. Their lengths can be up to 10^5, so they may not fit in standard integer types.

A positive integer is called parity balanced if the parity (even/odd) of the sum of digits at odd positions is the same as the parity of the sum of digits at even positions.

Positions are 1-indexed from the leftmost digit.

Your task is to determine how many parity balanced numbers lie in the inclusive range [L, R].

Since the answer can be large, print it modulo 10^9 + 7.

Input Format

The first line contains the string L. The second line contains the string R.

Output Format

Print a single integer — the number of parity balanced integers in [L, R] modulo 10^9 + 7.

Sample Input 10 20 Sample Output 6 Explanation

The valid numbers are:

11 13 15 17 19 20