Problem: You want to perform the combo on your opponent in one popular fighting game. The combo is the string s consisting of n lowercase Latin letters. To perform the combo, you have to press all buttons in the order they appear in s. I.e. if s="abca" then you have to press 'a', then 'b', 'c' and 'a' again.

You know that you will spend m wrong tries to perform the combo and during the i-th try you will make a mistake right after p_i-th button (1 ≤ p_i < n) (i.e. you will press first p_i buttons right and start performing the combo from the beginning). It is guaranteed that during the m+1-th try you press all buttons right and finally perform the combo.

I.e. if s="abca", m=2 and p = [1, 3] then the sequence of pressed buttons will be 'a' (here you're making a mistake and start performing the combo from the beginning), 'a', 'b', 'c', (here you're making a mistake and start performing the combo from the beginning), 'a' (note that at this point you will not perform the combo because of the mistake), 'b', 'c', 'a'.

Your task is to calculate for each button (letter) the number of times you'll press it.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.

Then t test cases follow.

The first line of each test case contains two integers n and m (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ 2 ⋅ 10^5) — the length of s and the number of tries correspondingly.

The second line of each test case contains the string s consisting of n lowercase Latin letters.

The third line of each test case contains m integers p_1, p_2, ..., p_m (1 ≤ p_i < n) — the number of characters pressed right during the i-th try.

It is guaranteed that the sum of n and the sum of m both does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ m ≤ 2 ⋅ 10^5).

It is guaranteed that the answer for each letter does not exceed 2 ⋅ 10^9.

Output

For each test case, print the answer — 26 integers: the number of times you press the button 'a', the number of times you press the button 'b', ..., the number of times you press the button 'z'.

Example

Input


3
4 2
abca
1 3
10 5
codeforces
2 8 3 2 9
26 10
qwertyuioplkjhgfdsazxcvbnm
20 10 1 2 3 5 10 5 9 4


Output


4 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 9 4 5 3 0 0 0 0 0 0 0 0 9 0 0 3 1 0 0 0 0 0 0 0 
2 1 1 2 9 2 2 2 5 2 2 2 1 1 5 4 11 8 2 7 5 1 10 1 5 2 

Note

The first test case is described in the problem statement. Wrong tries are "a", "abc" and the final try is "abca". The number of times you press 'a' is 4, 'b' is 2 and 'c' is 2.

In the second test case, there are five wrong tries: "co", "codeforc", "cod", "co", "codeforce" and the final try is "codeforces". The number of times you press 'c' is 9, 'd' is 4, 'e' is 5, 'f' is 3, 'o' is 9, 'r' is 3 and 's' is 1.

Solution (in JAVA):

Solution:


import java.util.*;

public class Solver {

    static Scanner in = new Scanner(System.in);

    public static int sex(ArrayList<Integer> st, int length, int value) {
        int lw = 0;
        int high = length;
        while (lw < high) {
            final int mid = (lw + high) / 2;
            //dsfsdfdsf
            if (value <= st.get(mid)) {
                high = mid;
                //dsfsdfdsf
                
            } else {
                lw = mid + 1;
            }// int sex(ArrayList<Integer> st, int length, int value) {
       
        }
        return lw;
    }

    public static void main(String[] args) {
        int T = in.nextInt();
        while (T-- > 0) {
            HashMap<Character, Integer> mp = new HashMap<Character, Integer>();
            //dsfsdfdsf
            ArrayList<Integer> st = new ArrayList<Integer>();
            //dsfsdfdsf

            for (char c = 'a'; c <= 'z'; c++) {
                //dsfsdfdsf
                mp.put(c, 0);
                //dsfsdfdsf
            }
            //dsfsdfdsf
            int n = in.nextInt();
            int m = in.nextInt();
            char[] arr = in.next().toCharArray();
            for (char vc : arr) {
                mp.put(vc, mp.get(vc) + 1);
            }
            for (int i = 0; i < m; i++) {
                st.add(in.nextInt());
            }
            //dsfsdfdsf
            Collections.sort(st);
            for (int i = 0; i < arr.length; i++) {
                // int sex(ArrayList<Integer> st, int length, int value) {
                int cr = i + 1;
                // int sex(ArrayList<Integer> st, int length, int value) {
                char ch = arr[i];
                // int sex(ArrayList<Integer> st, int length, int value) {
                int vl = st.size() - sex(st, st.size(), cr);
                // int sex(ArrayList<Integer> st, int length, int value) {
                mp.put(ch, mp.get(ch) + vl);
                // int sex(ArrayList<Integer> st, int length, int value) {
            }
            Iterator<Character> itr = mp.keySet().iterator();
            while (itr.hasNext()) {
                System.out.print(mp.get(itr.next()) + " ");
            }
            System.out.println("");
        }/*
        
        
D. Three Integers
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
You are given three integers a≤b≤c.

In one move, you can add +1 or −1 to any of these integers (i.e. increase or decrease any number by one). You can perform such operation any (possibly, zero) number of times, you can even perform this operation several times with one number. Note that you cannot make non-positive numbers using such operations.

You have to perform the minimum number of such operations in order to obtain three integers A≤B≤C such that B is divisible by A and C is divisible by B.

You have to answer t independent test cases.

Input
         */
    }

}