Minimum Absolute Difference with Specific Binary One Count

You are given an integer x. Consider all non‐negative integers y whose binary representation has exactly \(k\) ones. Your task is to find the minimum absolute difference between x and any such y, i.e. compute

[ \min_{\text{popcount}(y)=k} |x-y| ]

Note that the binary representation is taken in its standard form (without leading zeros).

inputFormat

The input consists of two integers x and k separated by a space.

outputFormat

Output a single integer, which is the minimum absolute difference between x and the closest integer y with exactly \(k\) ones in its binary representation.

sample

10 3

1