Problem: Ashish has two strings a and b, each of length n, and an integer k. The strings only contain lowercase English letters.

He wants to convert string a into string b by performing some (possibly zero) operations on a.

In one move, he can either 

  * choose an index i (1 ≤ i≤ n-1) and swap a_i and a_{i+1}, or 
  * choose an index i (1 ≤ i ≤ n-k+1) and if a_i, a_{i+1}, …, a_{i+k-1} are all equal to some character c (c ≠ 'z'), replace each one with the next character (c+1), that is, 'a' is replaced by 'b', 'b' is replaced by 'c' and so on. 



Note that he can perform any number of operations, and the operations can only be performed on string a. 

Help Ashish determine if it is possible to convert string a into b after performing some (possibly zero) operations on it.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. The description of each test case is as follows.

The first line of each test case contains two integers n (2 ≤ n ≤ 10^6) and k (1 ≤ k ≤ n).

The second line of each test case contains the string a of length n consisting of lowercase English letters.

The third line of each test case contains the string b of length n consisting of lowercase English letters.

It is guaranteed that the sum of values n among all test cases does not exceed 10^6.

Output

For each test case, print "Yes" if Ashish can convert a into b after some moves, else print "No".

You may print the letters of the answer in any case (upper or lower).

Example

Input


4
3 3
abc
bcd
4 2
abba
azza
2 1
zz
aa
6 2
aaabba
ddddcc


Output


No
Yes
No
Yes

Note

In the first test case it can be shown that it is impossible to convert a into b.

In the second test case,

"abba" \xrightarrow{inc} "acca" \xrightarrow{inc} … \xrightarrow{inc} "azza".

Here "swap" denotes an operation of the first type, and "inc" denotes an operation of the second type.

In the fourth test case,

"aaabba" \xrightarrow{swap} "aaabab" \xrightarrow{swap} "aaaabb" \xrightarrow{inc} … \xrightarrow{inc} "ddaabb" \xrightarrow{inc} … \xrightarrow{inc} "ddddbb" \xrightarrow{inc} … \xrightarrow{inc} "ddddcc".

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import static java.lang.Math.PI;
import static java.lang.System.in;
import static java.lang.System.out;

public class C {   
    public static void main(String[] args) throws Exception {   
        Foster sc = new Foster();
        PrintWriter p = new PrintWriter(out);
        int t = sc.nextInt();
        while(t--!=0){
            int n = sc.nextInt(), k = sc.nextInt();
            char a[] = sc.next().toCharArray();
            char b[] = sc.next().toCharArray();
            int freqA[] = new int[26];
            int freqB[] = new int[26];
            for(char ch : a){
                int idx = (int)(ch-'a');
                freqA[idx]++;
            }
            for(char ch : b){
                int idx = (int)(ch-'a');
                freqB[idx]++;
            }
            for(int i = 0; i < 26; i++){
                freqA[i] -= freqB[i];
            }
            boolean poss = true;
            for(int i = 0; i < 26; i++){
                if(freqA[i]%k!=0)    poss = false;
            }
            a = sort(a);
            b = sort(b);
            for(int i = 0; i < n; i++){
                if(a[i] > b[i]) poss = false;
            }
            p.println(poss ? "YES" : "NO");
        }
        p.close();
    }

    static char[] sort(char a[]){
        ArrayList<Character> arr = new ArrayList<>();
        for(char i : a){
            arr.add(i);
        }
        Collections.sort(arr);
        for(int i = 0; i < arr.size(); i++){
            a[i] = arr.get(i);
        }
        return a;
    }
/* 
*/    
/*
1. Check overflow in pow function or in general
2. Check indices of read array function
3. Think of an easier solution because the problems you solve are always easy
4. Check iterator of loop
5. If still doesn't work, then jump from the 729th floor 'coz "beta tumse na ho paayega"

    Move to top!!
*/
    static class Foster {
        BufferedReader br = new BufferedReader(new InputStreamReader(in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } 
                catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        int[] intArray(int n) {                   // Check indices
            int arr[] = new int[n];
            for(int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
        long[] longArray(int n) {                 // Check indices
            long arr[] = new long[n];
            for(int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }
        int[] getBits(int n) {                   //in Reverse Order
            int a[] = new int[31];
            for(int i = 0; i < 31; i++) {
                if(((1<<i) & n) != 0)
                    a[i] = 1;
            }
            return a;
        }
        static String reverse(String s){
            String temp = "";
            for(int i = s.length()-1; i >= 0; i--){
                temp += s.charAt(i);
            }
            return temp;
        }
        static long pow(long... a) {
            long mod = Long.MAX_VALUE;
            if(a.length == 3)   mod = a[2];
            long res = 1;
            while(a[1] > 0) {
                if((a[1] & 1) == 1)
                    res = (res * a[0]) % mod;
                a[1] /= 2;
                a[0] = (a[0] * a[0]) % mod;
            }
            return res;
        }
        static void print(Object... o) {
            for(Object next : o) {
                System.err.print(next + " ");
            }
        }
        static void println(Object... o) {
            for(Object next : o) {
                System.err.print(next + " ");
            }
            System.err.println();
        }
        static void watch(Object...a) throws Exception {
            int i = 1;
            for (Object o: a) {
                boolean found = false;
                if (o.getClass().isArray()) {
                    String type = o.getClass().getName().toString();
                    switch (type) {
                        case "[I": {
                            int[] test = (int[]) o;
                            println(i + " : " + Arrays.toString(test));
                            break;
                        }
                        case "[[I": {
                            int[][] obj = (int[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[J": {
                            long[] obj = (long[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[J": {
                            long[][] obj = (long[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[D": {
                            double[] obj = (double[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[D": {
                            double[][] obj = (double[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[Ljava.lang.String": {
                            String[] obj = (String[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[Ljava.lang.String": {
                            String[][] obj = (String[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[C": {
                            char[] obj = (char[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[C": {
                            char[][] obj = (char[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        default: {
                            println(i + " : type not identified");
                            break;
                        }
                    }
                    found = true;
                }
                if (o.getClass() == ArrayList.class) {
                    println(i + " : LIST = " + o);
                    found = true;
                }
                if (o.getClass() == TreeSet.class) {
                    println(i + " : SET = " + o);
                    found = true;
                }
                if (o.getClass() == TreeMap.class) {
                    println(i + " : MAP = " + o);
                    found = true;
                }
                if (o.getClass() == HashMap.class) {
                    println(i + " : MAP = " + o);
                    found = true;
                }
                if (o.getClass() == LinkedList.class) {
                    println(i + " : LIST = " + o);
                    found = true;
                }
                if (o.getClass() == PriorityQueue.class) {
                    println(i + " : PQ = " + o);
                    found = true;
                }
                if (!found) {
                    println(i + " = " + o);
                }
                i++;
            }
        }
    }
}