F. Subsequences of Length Two
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You 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 $15$.