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Contest: Task: Related: TaskF TaskH

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.

Sample Input 1

YY...Y.Y.Y.
2

Sample Output 1

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 $3$.

Sample Input 2

YYYY....YYY
3