Minimum Operations to Equalize Two Numbers

Given two positive integers \(a\) and \(b\), you can perform one of the following operations in each move:

• \(a \gets a \times 2\)
• \(b \gets b - 1\)
• \(b \gets b + 1\)

The goal is to make \(a = b\) with the minimum number of operations. One way to solve the problem is to consider the number of times you double \(a\) (say \(k\) times) so that \(a \times 2^k\) is as close as possible to \(b\), and then adjust \(b\) with the necessary increments or decrements. The total operations would be \(k + \left|a \times 2^k - b\right|\), and you should choose the minimum over all possible \(k\).

inputFormat

The input consists of a single line with two space-separated positive integers \(a\) and \(b\).

\(1 \leq a, b \leq 10^{9}\)

outputFormat

Output a single integer representing the minimum number of operations required to make \(a = b\).

sample

3 10

4