Problem: 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 ≤ n ≤ 200; 0 ≤ k ≤ 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.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws Exception {

        new Main().go();
    }

    PrintWriter out;
    Reader in;
    BufferedReader br;

    Main() throws IOException {

        try {

            //br = new BufferedReader( new FileReader("input.txt") );
            //in = new Reader("input.txt");
            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            //br = new BufferedReader( new InputStreamReader( System.in ) );
            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }
    }

    void go() throws Exception {

        //int t = in.nextInt();
        int t = 1;
        while (t > 0) {
            solve();
            t--;
        }

        out.flush();
        out.close();
    }


    int inf = 2000000000;
    int mod = 1000000007;
    double eps = 0.000000001;

    int n;
    int m;

    ArrayList<Integer>[] g;
    int[] a;
    void solve() throws IOException {
        int t = 1;
        while (t > 0) {
            solveCase();
            t--;
        }
    }

    void solveCase() throws IOException {
        int n = in.nextInt();
        int k = in.nextInt();
        String s = in.next();
        String t = in.next();
        char first = t.charAt(0);
        char second = t.charAt(1);

        if (first == second) {
            int cnt = 0;
            for (int i = 0; i < n; i++)
                if (s.charAt(i) == first)
                    cnt++;
            cnt += Math.min(n - cnt, k);
            out.println(cnt * (cnt - 1) / 2);
            return;
        }

        int[][][] dp = new int[n + 1][k + 1][n + 1];

        for (int i = 0; i <= n; i++)
            for (int j = 0; j<= k; j++)
                for (int l = 0; l <= n; l++)
                    dp[i][j][l] = -1;

        dp[0][0][0] = 0;

        for (int i = 0; i < n; i++) {
            char cur = s.charAt(i);
            for (int cnt = 0; cnt <= k; cnt++)
                for (int j = 0; j <= n; j++) {

                    if (dp[i][cnt][j] == -1) continue;

                    dp[i + 1][cnt][j] = Math.max(dp[i][cnt][j], dp[i + 1][cnt][j]);

                    //System.err.println(i + " " + cnt + " " + j + " " + dp[i][cnt][j]);

                    if (cur != first && cnt + 1 <= k)
                        dp[i + 1][cnt + 1][j + 1] = Math.max(dp[i + 1][cnt + 1][j + 1], dp[i][cnt][j]);
                    else if (cur == first)
                        dp[i + 1][cnt][j + 1] = Math.max(dp[i + 1][cnt][j + 1], dp[i][cnt][j]);

                    if (cur != second && cnt + 1 <= k)
                        dp[i + 1][cnt + 1][j] = Math.max(dp[i + 1][cnt + 1][j], dp[i][cnt][j] + j);
                    else if (cur == second)
                        dp[i + 1][cnt][j] = Math.max(dp[i + 1][cnt][j], dp[i][cnt][j] + j);
                }
        }

        int ans = 0;
        for (int i = 0; i <= n; i++)
            for (int j = 0; j <= k; j++)
                for (int l = 0; l <= n; l++)
                    ans = Math.max(dp[i][j][l], ans);

        out.println(ans);
    }


    static class Pair<A extends Comparable<A>, B extends Comparable<B>> implements Comparable<Pair<A, B>> {

        public final A a;
        public final B b;

        Pair(A a, B b) {
            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair<A, B> p) {
            if (!a.equals(p.a))
                return a.compareTo(p.a);
            else
                return b.compareTo(p.b);
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }


    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }


        String nextLine() throws IOException {
            return br.readLine();
        }

    }

    static class InputReader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public InputReader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public InputReader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }

}