Junpyo's Pebbles

Time limit1sMemory limit512 MB

Summary

Find the longest contiguous segment containing at most B black pebbles and at least W white pebbles.

Level: Medium6 of 10
Topics: Two pointers, Sliding window, Prefix sum
Solved: No attempts yet

Problem

$N$ pebbles stand in a row, numbered from $1$ to $N$ . Each pebble is black or white.

Junpyo chooses one contiguous segment and picks up every pebble inside it. The segment may be empty, which means going straight home. Its length is the number of pebbles it contains.

A segment is valid when it holds at most $B$ black pebbles and at least $W$ white pebbles. If no valid segment exists, the answer is $0$ . Find the length of the longest valid segment.

Input

The first line contains $N$ , the upper bound $B$ for black pebbles, and the lower bound $W$ for white pebbles, separated by spaces.

The second line contains a string of length $N$ . Its $i$ -th character describes pebble $i$ : B means black and W means white.

Output

Print the length of the longest valid segment on one line. If no segment satisfies the conditions, print $0$ .

Examples2

Example 1
Input
```
10 1 2
WBBWWBWWBW
```
Expected output
```
5
```
Example 2
Input
```
7 2 4
WBBBBBW
```
Expected output
```
0
```