Background

Dun Dun invites you to evenly split sausages.

Problem Description

There are $n$ sausages, and they need to be evenly divided among $m$ tasters.

Each cut can split a sausage into two parts. You need to use as few cuts as possible to obtain sausages that meet the requirement. Find the minimum number of cuts needed.

Input Format

The input consists of one line with two positive integers $n$ and $m$.

Output Format

Output one line with the minimum number of cuts.

2 6

4

3 4

3

6 2

0

Hint

Sample Explanation

Sample 1 Explanation

There are $2$ sausages and $6$ tasters. Cut each sausage into three equal parts, which takes $4$ cuts.

Sample 2 Explanation

There are $3$ sausages and $4$ tasters. Cut the sausages into pieces of size $\tfrac{3}{4}$. The first three people each get $\tfrac{3}{4}$, and the last person gets $3\times \tfrac{1}{4}$.

Constraints

For all test cases, it is guaranteed that $1\le n,m\le 100$.

Notes

This problem is translated from COCI2013-2014 CONTEST #1 T2 KUŠAČ.

Translated by ChatGPT 5