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:
//package cf667;

import java.io.*;
import java.util.*;
import java.util.stream.Collectors;

public class F {
    static boolean CONSTRUCTIVE = false;
    static long MOD = (long) 1e9 + 7;
    static long BIG = (long) 2e9;

    public static void solve(Reader in, PrintWriter out) {
        int n = in.nextInt();
        int K = in.nextInt();
        char[] arr = in.next().toCharArray();
        String t = in.next();
        char a = t.charAt(0);
        char b = t.charAt(1);

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

        for (int i = 0; i < n; i++) {
            for (int k = 0; k <= K; k++) {
                for (int j = 0; j < n; j++) {
                    dp[i][k][j] = Integer.MIN_VALUE/2;
                }
            }
        }

        // index, k, as

        // first element
        if (arr[0] == a) {
            dp[0][0][1] = 0;
        } else {
            if (K > 0) dp[0][1][1] = 0;
            dp[0][0][0] = 0;
        }

        int max = 0;
        for (int i = 1; i < n; i++) {
            for (int k = 0; k <= K; k++) {
                for (int j = 0; j < n; j++) {
                    int val = dp[i-1][k][j];
                    // do nothing
                    if (arr[i] == a && j > 0) {
                        val = Math.max(val, a==b ? dp[i-1][k][j-1] + j-1 : dp[i - 1][k][j-1]); // get an a for free
                    }
                    if (arr[i] == b) {
                        val = Math.max(val, dp[i - 1][k][j] + j);
                    }

                    // change to a
                    if (k > 0 && j > 0) {
                        val = Math.max(val, a==b ? dp[i-1][k-1][j-1] + j-1 : dp[i - 1][k - 1][j - 1]);
                    }
                    // change to b
                    if (k > 0) {
                        val = Math.max(val, dp[i - 1][k - 1][j] + j);
                    }

                    dp[i][k][j] = val;
                    max = Math.max(max, val);
//                    if (a==b) System.out.printf("(%d %d %d): %d\n", i,k,j,val);
                }
            }
        }

        out.println(max);
    }

    public static void main(String[] args) throws IOException {
        Reader in = null;
        PrintWriter out = null;
        for (String arg : args) {
            if (arg.startsWith("input")) {
                in = new Reader(arg);
            } else if (arg.startsWith("output")) {
                out = new PrintWriter(new FileWriter(arg));
            }
        }
        if (in == null) in = new Reader();
        if (out == null) out = new PrintWriter(new OutputStreamWriter(System.out));

//        int tests = in.nextInt();
//        for (int t = 0; t < tests; t++) {
        solve(in, out);
//        }

        out.flush();
    }

    static class Tester {
        public static void main(String[] args) throws IOException {
            Validator validator = new Validator();

            System.out.println("SAMPLE TESTS:");
            File currentDir = new File(".");
            long before;
            long after;
            for (File inputFile : Arrays.stream(currentDir.listFiles())
                    .sorted(Comparator.comparing(File::getName))
                    .collect(Collectors.toList())) {
                if (!inputFile.getName().matches("input[0-9]")) continue;
                int number = Integer.parseInt(inputFile.getName().substring(5));
                System.out.printf("Test %d: \n", number);

                before = System.nanoTime();
                String outputFileName = "output" + inputFile.getName().substring(5);
                F.main(new String[]{inputFile.getName(), outputFileName});
                after = System.nanoTime();

                File outputFile = new File("output" + number);
                if (!outputFile.exists()) {
                    throw new IllegalStateException("Missing output file " + outputFile);
                }

                // TODO if verifier is implemented, remove this
                if (CONSTRUCTIVE) {
                    System.out.println("INPUT:");
                    printFile(inputFile);
                    System.out.printf("\nOUTPUT: (%d milliseconds)\n", (after - before) / 1000000L);
                    printFile(outputFile);
                    continue;
                }

                if (validator.validate(inputFile, outputFile)) {
                    System.out.printf("OK (%d milliseconds)\n", (after - before) / 1000000L);
                } else {
                    System.out.println("FAILED");
                    System.out.println("\nInput: ");
                    printFile(inputFile);
                    System.out.println("\nIncorrect Output: ");
                    printFile(outputFile);
                    return;
                }
            }
            System.out.println("\n-----------------\n");

            File sightTestInput = new File("input-sight");
            if (sightTestInput.exists()) {
                System.out.println("Running sight test... Input:");
                printFile(sightTestInput);
                before = System.nanoTime();
                System.out.println("\nOutput: ");
                F.main(new String[]{"input-sight"});
                after = System.nanoTime();
                System.out.printf("(%d milliseconds)\n", (after - before) / 1000000L);
                System.out.println("\n-----------------\n");
            }

            File bigTestInput = new File("input-big");
            if (bigTestInput.exists()) {
                System.out.println("Running big test...");
                before = System.nanoTime();
                F.main(new String[] {"input-big"});
                after = System.nanoTime();
                System.out.printf("(%d milliseconds)\n", (after - before) / 1000000L);
            }
        }

        static void printFile(File file) throws FileNotFoundException {
            BufferedReader reader = new BufferedReader(new FileReader(file));
            reader.lines().forEach(System.out::println);
        }
    }

    static class Validator {
        boolean validate(File inputFile, File outputFile) throws IOException {
            int number = Integer.parseInt(inputFile.getName().substring(5));
            File expectedOutputFile = new File("expected-output" + number);
            if (CONSTRUCTIVE || !expectedOutputFile.exists()) {
                return validateManual(inputFile, outputFile);
            }
            return areSame(outputFile, expectedOutputFile);
        }

        private boolean validateManual(File inputFile, File outputFile) throws IOException {
            // OPTION 1: validate against naive solution
//            Naive.main(new String[] {inputFile.getName()})


            // OPTION 2: Validate output against input (typically for constructive problems)
            Reader inputReader = new Reader(inputFile.getName());
            Reader outputReader = new Reader(outputFile.getName());

            // TODO implement manual validation

            throw new IllegalStateException("Missing expected output file");
        }

        private boolean areSame(File file1, File file2) throws IOException {
            BufferedReader reader1 = new BufferedReader(new FileReader(file1));
            BufferedReader reader2 = new BufferedReader(new FileReader(file2));

            String line1;
            while ((line1 = reader1.readLine()) != null) {
                String line2 = reader2.readLine();
                if (line2 == null) line2 = ""; // ok if one has an extra newline
                if (!line1.trim().equals(line2.trim())) {
                    return false;
                }
            }
            String line2;
            while ((line2 = reader2.readLine()) != null) {
                if (!line2.trim().isEmpty()) {
                    return false;
                }
            }
            return true;
        }

    }

    static class Naive {
        public static void solveNaive(Reader in, PrintWriter out) {

        }

        public static void main(String[] args) throws IOException {
            Reader in = null;
            PrintWriter out = null;
            for (String arg : args) {
                if (arg.startsWith("input")) {
                    in = new Reader(arg);
                } else if (arg.startsWith("output")) {
                    out = new PrintWriter(new FileWriter(arg));
                }
            }
            if (in == null) in = new Reader();
            if (out == null) out = new PrintWriter(new OutputStreamWriter(System.out));

            int tests = in.nextInt();
            for (int t = 0; t < tests; t++) {
                solve(in, out);
            }

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

    static long pair(int x, int y) {
        return x * BIG + y;
    }

    static int x(long pair) {
        return (int) (pair / BIG);
    }

    static int y(long pair) {
        return (int) (pair % BIG);
    }

    static class Reader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public Reader(String fileName) throws FileNotFoundException {
            reader = new BufferedReader(new FileReader(fileName));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int[] nextInts(int n) {
            int[] out = new int[n];
            for (int i = 0; i < n; i++) {
                out[i] = nextInt();
            }
            return out;
        }

        public long[] nextLongs(int n) {
            long[] out = new long[n];
            for (int i = 0; i < n; i++) {
                out[i] = nextLong();
            }
            return out;
        }
    }
}