Score : $600$ points

Problem Statement

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

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

• Swap two adjacent characters in $S$.

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

Constraints

• $2 \leq |S| \leq 2 \times 10^5$
• Each character of $S$ is Y or ..
• $0 \leq K \leq 10^{12}$
• $K$ is an integer.

Input

Input is given from Standard Input in the following format:

$S$

$K$

Output

Print the answer.

YY...Y.Y.Y.
2

3

After swapping the $6$-th, $7$-th characters, and $9$-th, $10$-th characters, we have YY....YYY.., which has three consecutive Ys at $7$-th through $9$-th positions. We cannot have four or more consecutive Ys, so the answer is $3$.

YYYY....YYY
3

4