Minimum Cost Bitwise Transformation

You are given two positive integers n and m. In one operation, you can choose one of the following two actions on n at a cost of 1:

• ACCEPT: Replace n with n | k, where k is any positive integer. Here, | denotes the bitwise OR operation.
• BOTH: Replace n with n & k, where k is any positive integer. Here, & denotes the bitwise AND operation.

Your task is to determine the minimum cost required to transform n into m using a sequence of these operations (operations may be performed zero or more times).

Note: The operations work on the binary representations of the numbers. In particular:

• The OR operation, n = n | k, can only set bits to 1 (it cannot clear bits already set in n).
• The AND operation, n = n & k, can only clear bits to 0 (it cannot set 0 bits to 1).

Thus, if n already has extra bits (1's) that m does not have, you can clear them using the BOTH operation. Conversely, if n lacks some bits that m has, you can set them using the ACCEPT operation.

Hint (in LaTeX):

\( \text{If } n = m, \text{ the cost is } 0. \)

\( \text{If } n \subseteq m \text{ (i.e. } n \text{ has no bits that are 1 while } m \text{ has 0), then one ACCEPT operation is enough.} \)

\( \text{If } m \subseteq n \text{ (i.e. } m \text{ has no bits that are 1 while } n \text{ has 0), then one BOTH operation is enough.} \)

\( \text{Otherwise, the answer is } 2. \)

inputFormat

The input consists of a single line with two space-separated positive integers n and m.

\(1 \leq n, m \leq 10^9\)

outputFormat

Output a single integer, the minimum cost required to transform n into m using the allowed operations.

sample

3 3

0