Problem Description

For a positive integer $x$, let $rev(x)$ denote the integer obtained by reversing the digits of $x$ when $x$ is written in base 10. For example, $rev(123)=321$, $rev(90)=9$, and $rev(5)=5$.

You are given positive integers $N$ and $M$. Find the number of pairs of integers $(x, y)$ such that $1 \leq x \leq N$ and $1 \leq y \leq M$, and starting from $(x, y)$, the following sequence of operations can be performed infinitely:

• If either $x$ or $y$ is $0$, the process ends.
• If $x < y$, replace $x$ with $rev(x)$; otherwise, replace $y$ with $rev(y)$.
• After the above operation, if $x < y$, replace $y$ with $y - x$; otherwise, replace $x$ with $x - y$.

Input Format

The input is given from the standard input in the following format:

$N$ $M$

Output Format

Output the number of pairs $(x, y)$ such that starting from $(x, y)$, the operations can be performed infinitely.

Sample Input and Output

Sample Input #1

13 13

Sample Output #1

1

Sample Input #2

20 30

Sample Output #2

28

Sample Input #3

314 159

Sample Output #3

1915

Notes/Hints

Constraints

• $1 \leq N, M \leq 999$
• All inputs are integers.

Sample Explanation 1

The pair $(13, 13)$ satisfies the condition. Specifically, the operations proceed as $(13, 13) \rightarrow (13, 18) \rightarrow (13, 18) \rightarrow \ldots$ and continue indefinitely.

见题面 Input 部分

见题面 Output 部分