Score : $400$ points

Problem Statement

Given is a string $S$ consisting of X and ..

You can do the following operation on $S$ between $0$ and $K$ times (inclusive).

• Replace a . with an X.

What is the maximum possible number of consecutive Xs in $S$ after the operations?

Constraints

• $1 \leq |S| \leq 2 \times 10^5$
• Each character of $S$ is X or ..
• $0 \leq K \leq 2 \times 10^5$
• $K$ is an integer.

Input

Input is given from Standard Input in the following format:

$S$

$K$

Output

Print the answer.

XX...X.X.X.
2

5

After replacing the Xs at the $7$-th and $9$-th positions with X, we have XX...XXXXX., which has five consecutive Xs at $6$-th through $10$-th positions. We cannot have six or more consecutive Xs, so the answer is $5$.

XXXX
200000

4

It is allowed to do zero operations.