Champernowne Count

문제

The $n$th Champernowne word is obtained by writing down the first $n$ positive integers and concatenating them together. For example, the 10th Champernowne word is "12345678910".

Given two positive integers $n$ and $k$, count how many of the first $n$ Champernowne words are divisible by $k$.

입력

The single line of input contains two integers, $n$ $(1\le n\le {10}^5)$ and $k$ $(1\le k\le {10}^9)$.

출력

Output a single integer, which is a count of the first $n$ Champernowne words divisible by $k$.

예제 입력 1 복사

4 2

예제 입력 2 복사

100 7

예제 입력 3 복사

314 159

예제 입력 4 복사

100000 999809848

예제 출력 1 복사

2

예제 출력 2 복사

14

예제 출력 3 복사

4

예제 출력 4 복사

1