You are given a binary string \(s\) of size \(n\) containing only 0s and 1s. A substring of size \(k\) is called good if the count of all 1s in this substring is not greater than \(m\).

You are required to transform a string in such a manner that every substring of size \(k\) are good by performing some operations. In one operation, you can change the value of a character in a string from 1 to 0.

Determine the minimum number of operations that are required such that every substring of size \(k\) in the given string is good.

Input format

First line: Three space-separated integers \(n\), \(k\), and \(m\)
Second line: Binary string \(s\) of size \(n\)

Output format

First line: Print a single integer that denotes the minimum number of operations that are required.
Second line: Print the strings that are transformed after applying the operations. If there are multiple such strings, then you can print any of them.

Constraints

\(1 \leq k \leq n \leq 10^{5}\)

\(0 \leq m \leq k\)