Score : $300$ points

Problem Statement

For a positive integer $x$, let $f(x)$ be the answer to the question below.

The following operation on $x$ can be performed zero or more times.

• Let $x'$ be the integer obtained by reversing the decimal notation of $x$. Then, replace $x$ with $x'$. If $x$ now has one or more leading zeros, delete them so that it begins with a non-zero digit.

For example, from $x=1420$, you get $x=241$ after one operation, $x=142$ after two operations, and $x=241$ after three operations. Find the minimum possible value of $x$ after operations.

Find the number of integers $x$ such that $1 \leq x \leq N$ and $f(x)=K$.

Constraints

• $1 \leq N,K \leq 10^{12}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

Output

Print the answer.

1420 142

3

Three integers $x=142$, $241$, and $1420$ satisfy $1 \leq x \leq 1420$ and $f(x)=142$.

1419 142

2

6 19

0