Multiply or Subtract

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.

Examples

Input
Output
10 1
9
4 6
2

Explanation

  1. Subtract 1 from 10 9 times
  1. 4 β†’ 3 (subtract 1) β†’ 6 (multiply by 2)
Β 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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