You are given two numbers - start s and target t. You’d like to get to the target number t starting from s by only multiplying the current number by 2 or subtracting 1 from it.

What would be the minimum number of operations to get from s to t?

Input

The first line of the input contains 2 integers s and t (1 ≤ s, t ≤ 10 000).

Output

The program should print the minimum number of operations to get from s to t.