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:
//package codeforces.round624div3;

import java.io.*;
import java.util.*;

public class PerformCombo {
    private static int UNVISITED = 0;
    private static int VISITING = -1;
    private static int VISITED = 1;

    public static void main(String[] args) {
//        try {
//            FastScanner in = new FastScanner(new FileInputStream("src/input.in"));
//            PrintWriter out = new PrintWriter(new FileOutputStream("src/output.out"));

        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

            int t = in.nextInt();
            solve(t, in, out);

//        } catch (IOException e) {
//            e.printStackTrace();
//        }
    }

    private static void solve(int q, FastScanner in, PrintWriter out) {
        for (int qq = 0; qq < q; qq++) {
            int n = in.nextInt();
            int m = in.nextInt();
            String s = in.next();
            int[] p = new int[m];
            for(int i = 0; i < m; i++) {
                p[i] = in.nextInt() - 1;
            }
            int[][] ps = new int[n][26];
            for(int i = 0; i < n; i++) {
                for(int j = 0; j < 26; j++) {
                    if(s.charAt(i) - 'a' == j) {
                        ps[i][j] = (i > 0 ? ps[i - 1][j] : 0) + 1;
                    }
                    else {
                        ps[i][j] = (i > 0 ? ps[i - 1][j] : 0);
                    }
                }
            }
            int[] ans = new int[26];
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < 26; j++) {
                    ans[j] += ps[p[i]][j];
                }
            }
            for(int j = 0; j < 26; j++) {
                ans[j] += ps[n - 1][j];
            }
            for(int j = 0; j < 26; j++) {
                out.print(ans[j] + " ");
            }
            out.println();
        }
        out.close();
    }

    private static long modularAdd(long a, long b, int mod) {
        long sum = a + b;
        if (sum >= mod) {
            sum -= mod;
        }
        return sum;
    }

    private static long modularSubtract(long a, long b, int mod) {
        long diff = a - b;
        if (diff < 0) {
            diff += mod;
        }
        return diff;
    }

    private static Stack<Integer> topologicalSort(Set<Integer>[] g) {
        Stack<Integer> stack = new Stack<>();
        int[] state = new int[g.length];

        for (int node = 0; node < g.length; node++) {
            if (!topoSortHelper(g, stack, state, node)) {
                return null;
            }
        }
        return stack;
    }

    private static boolean topoSortHelper(Set<Integer>[] g, Stack<Integer> stack, int[] state, int currNode) {
        if (state[currNode] == VISITED) {
            return true;
        } else if (state[currNode] == VISITING) {
            return false;
        }
        state[currNode] = VISITING;
        for (int neighbor : g[currNode]) {
            if (!topoSortHelper(g, stack, state, neighbor)) {
                return false;
            }
        }
        state[currNode] = VISITED;
        stack.push(currNode);
        return true;
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !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());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}