Kawashiro Nitori is a girl who loves competitive programming.

One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem.

Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ 

Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped.

Input

The input consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 100) — the number of test cases. The description of the test cases follows.

The first line of each test case description contains two integers n, k (1≤ n≤ 100, 0≤ k≤ ⌊ n/2 ⌋) — the length of the string s and the parameter k.

The second line of each test case description contains a single string s of length n, consisting of lowercase English letters.

Output

For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise.

You can print letters in any case (upper or lower).

Example

Input


7
5 1
qwqwq
2 1
ab
3 1
ioi
4 2
icpc
22 0
dokidokiliteratureclub
19 8
imteamshanghaialice
6 3
aaaaaa


Output


YES
NO
YES
NO
YES
NO
NO

Note

In the first test case, one possible solution is a_1=qw and a_2=q.

In the third test case, one possible solution is a_1=i and a_2=o.

In the fifth test case, one possible solution is a_1=dokidokiliteratureclub.
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class CF706Div2A {

    static class FastReader {
        final private int BUFFER_SIZE = 1 << 17;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

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

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

        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;
        }

        public int[] nextIntArray(int size) throws IOException {
            int[] arr = new int[size];
            for (int i = 0; i < size; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int size) throws IOException {
            long[] arr = new long[size];
            for (int i = 0; i < size; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        public int[][] nextIntMatrix(int n, int m) throws IOException {
            int[][] arr = new int[n][m];
            for (int i = 0; i < n; i++) {
                arr[i] = nextIntArray(m);
            }
            return arr;
        }

        public long[][] nextLongMatrix(int n, int m) throws IOException {
            long[][] arr = new long[n][m];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLongArray(m);
            }
            return arr;
        }

        public ArrayList<Integer> nextIntList(int size) throws IOException {
            ArrayList<Integer> arrayList = new ArrayList<>(size);
            for (int i = 0; i < size; i++) {
                arrayList.add(nextInt());
            }
            return arrayList;
        }

        public ArrayList<Long> nextLongList(int size) throws IOException {
            ArrayList<Long> arrayList = new ArrayList<>(size);
            for (int i = 0; i < size; i++) {
                arrayList.add(nextLong());
            }
            return arrayList;
        }

        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();
        }
    }

    static class FastPrinter {
        final private PrintWriter out;

        FastPrinter() {
            out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        }

        public void printlnArray(int[] arr) {
            for (int i : arr) {
                out.println(i);
            }
        }

        public void printlnArray(long[] arr) {
            for (long i : arr) {
                out.println(i);
            }
        }

        public void printArray(int[] arr) {
            for (int i : arr) {
                out.print(i + " ");
            }
            out.println();
        }

        public void printArray(long[] arr) {
            for (long i : arr) {
                out.print(i + " ");
            }
            out.println();
        }

        public void println() {
            out.println();
        }

        public void println(String s) {
            out.println(s);
        }

        public void println(int s) {
            out.println(s);
        }

        public void println(long s) {
            out.println(s);
        }

        public void println(double s) {
            out.println(s);
        }

        public void print(String s) {
            out.print(s);
        }

        public void print(long s) {
            out.print(s);
        }

        public void print(int s) {
            out.print(s);
        }

        public void print(char s) {
            out.print(s);
        }

        public void close() {
            out.flush();
            out.close();
        }
    }

    final static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    final static StringBuilder ans = new StringBuilder();

    public static void main(String[] args) {
        try {
            long startTime = System.currentTimeMillis();
            final FastPrinter fp = new FastPrinter();
            // Write code here---

            for (int test = Integer.parseInt(br.readLine()); test > 0; test--) {
                StringTokenizer st = new StringTokenizer(br.readLine());
                int n = Integer.parseInt(st.nextToken());
                int k = Integer.parseInt(st.nextToken());
                String s = br.readLine();
                solution(n, k, s, fp);
            }

            fp.println(ans.toString());

            long endTime = System.currentTimeMillis();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                fp.println("Time: " + (endTime - startTime) + " ms");
            }

            fp.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private static void solution(int n, int k, String s, CF706Div2A.FastPrinter fp) {
        if (k == 0) {
            ans.append("YES").append('\n');
            return;
        }
        if (k * 2 >= n) {
            ans.append("NO").append('\n');
            return;
        }
        boolean pal = isPalindrome(s, k);
        ans.append(pal ? "YES" : "NO").append('\n');
    }

    private static boolean isPalindrome(String s, int k) {
        int n = s.length() - 1;
        for (int i = 0; i < k; i++) {
            if (s.charAt(i) != s.charAt(n - i)) {
                return false;
            }
        }
        return true;
    }

}
