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F. Subsequences of Length Two

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given two strings $$$s$$$ and $$$t$$$ consisting of lowercase Latin letters. The length of $$$t$$$ is $$$2$$$ (i.e. this string consists only of two characters).

In one move, you can choose any character of $$$s$$$ and replace it with any lowercase Latin letter. More formally, you choose some $$$i$$$ and replace $$$s_i$$$ (the character at the position $$$i$$$) with some character from 'a' to 'z'.

You want to do no more than $$$k$$$ replacements in such a way that maximizes the number of occurrences of $$$t$$$ in $$$s$$$ as a subsequence.

Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.

Input

The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 200$$$; $$$0 \le k \le n$$$) — the length of $$$s$$$ and the maximum number of moves you can make. The second line of the input contains the string $$$s$$$ consisting of $$$n$$$ lowercase Latin letters. The third line of the input contains the string $$$t$$$ consisting of two lowercase Latin letters.

Output

Print one integer — the maximum possible number of occurrences of $$$t$$$ in $$$s$$$ as a subsequence if you replace no more than $$$k$$$ characters in $$$s$$$ optimally.

Examples

Input

4 2 bbaa ab

Output

3

Input

7 3 asddsaf sd

Output

10

Input

15 6 qwertyhgfdsazxc qa

Output

16

Input

7 2 abacaba aa

Output

15

Note

In the first example, you can obtain the string "abab" replacing $$$s_1$$$ with 'a' and $$$s_4$$$ with 'b'. Then the answer is $$$3$$$.

In the second example, you can obtain the string "ssddsdd" and get the answer $$$10$$$.

In the fourth example, you can obtain the string "aaacaaa" and get the answer $$$15$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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