Background

Original problem link: https://oier.team/problems/X7B.

There used to be a rather bizarre background story hinting at modern marketing accounts, but it was deleted because it was too bizarre.

Problem Description

Given two positive integers $a$ and $b$, you may choose one of the following operations each time:

1. $a\gets a\times 2$.
2. $b\gets b-1$.
3. $b\gets b+1$.

Find the minimum number of operations needed to make $a=b$.

Input Format

Only one line with two positive integers $a,b$.

Output Format

Only one line with one non-negative integer, representing the minimum number of operations.

1 5

3

114514 1919810

87590

Hint

Sample Explanation #1

Initially, $a=1$ and $b=5$.

• Perform operation $1$, resulting in $a=2$, $b=5$.
• Perform operation $1$, resulting in $a=4$, $b=5$.
• Perform operation $2$, resulting in $a=4$, $b=4$.

The total number of operations is $3$. It can be proven that there is no solution with fewer operations.

Constraints

For $28\%$ of the testdata, $a,b\le 20$.

For $60\%$ of the testdata, $a,b\le 5000$.

For all testdata, $1\le a,b\le 10^9$.

Translated by ChatGPT 5