Binary String Transformation under Budget

You are given two binary strings: an initial string and a target string, both of length \(n\). The transformation cost is defined as the number of positions where the two strings differ, mathematically expressed as \(\text{cost} = \sum_{i=1}^{n} \mathbb{1}_{\{initial_i \neq target_i\}}\). You are also provided with a budget \(b\). Your task is to determine whether the initial string can be transformed into the target string within the given budget. If \(\text{cost} \le b\), output "YES"; otherwise, output "NO".

Input/Output Format: The input is read from standard input (stdin) and output should be printed to standard output (stdout).

inputFormat

The input is given from standard input in the following format:

n b
initial
target

where:

• n is an integer representing the length of the strings,
• b is an integer representing the budget,
• initial is the initial binary string of length n,
• target is the target binary string of length n.

outputFormat

The output, printed to standard output, is a single line containing either "YES" if the transformation can be done within the budget or "NO" if it cannot.

5 3
11000
10011

YES