Counting Numbers with Exactly K Ones in Binary

Little Blue is learning binary numbers. He is curious about how many numbers between \(1\) and \(N\) inclusive have exactly \(K\) ones in their binary representation. Can you help him?

Task: Given two integers \(N\) and \(K\), count the numbers from \(1\) to \(N\) whose binary representation contains exactly \(K\) ones.

Note: If a number's binary representation includes leading zeros, they are not counted. For example, the binary representation of \(3\) is 11 which has two ones, so if \(K = 2\), \(3\) should be counted.

inputFormat

The input consists of a single line containing two space-separated integers \(N\) and \(K\). For example:
10 2

outputFormat

Output a single integer which is the count of numbers between \(1\) and \(N\) (inclusive) that have exactly \(K\) ones in their binary representation.

sample

10 2

5