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.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.stream.Collectors;

public class Main {
    private static FastScanner input;
    private static PrintWriter output;

    public static void main(String[] args) throws IOException {
//        openFile();
        openConsole();

        int numTest = readInt();
        for (int i = 0; i < numTest; i++) {
            int wordLen = readInt();
            int tryLen = readInt();
            String line = readString();
            int[] pref = new int[wordLen];
            int[] count = new int[26];
            int[] tries = new int[tryLen];
            for (int each_try = 0; each_try < tryLen; each_try++) {
                int len = readInt();
                tries[each_try] = len;
                ++pref[len - 1];
            }
//            System.out.println(Arrays.toString(tries));
//            System.out.println("Pref-1: " + Arrays.toString(pref));

            for (int j = wordLen - 1; j > 0; j--) {
                pref[j - 1] += pref[j];
            }
//            System.out.println("Pref-2: " + Arrays.toString(pref));

            for (int j = 0; j < wordLen; j++) {
                count[line.charAt(j) - 'a'] += (pref[j] + 1);
            }

            String result = Arrays.stream(count)
                    .mapToObj(aElem -> ("" + aElem))
                    .collect(Collectors.joining(" "));
            output.println(result);
        }
        closeReader();
    }


    private static void solveC() throws IOException {
        int numTest = readInt();
        for (int i = 0; i < numTest; i++) {
            int a = readInt();
            int b = readInt();
            int c = readInt();
            int aRes = 0, bRes = 0, cRes = 0, count = Integer.MAX_VALUE;
            for (int aIter = 1; aIter <= 2 * a; aIter++) {
                for (int bIter = aIter; bIter <= 2 * b; bIter += aIter) {
                    int cLow = bIter * (c / bIter);
                    int cHigh = cLow + bIter;
                    int aAndBDist = Math.abs(aIter - a) + Math.abs(bIter - b);
                    int firstSum = aAndBDist + Math.abs(cLow - c);
                    int secondSum = aAndBDist + Math.abs(cHigh - c);
                    if (firstSum < count) {
                        aRes = aIter;
                        bRes = bIter;
                        cRes = cLow;
                        count = firstSum;
                    }
                    if (secondSum < count) {
                        aRes = aIter;
                        bRes = bIter;
                        cRes = cHigh;
                        count = secondSum;
                    }
                }
            }
            output.println(count);
            output.println(aRes + " " + bRes + " " + cRes);
        }
    }

    private static String readString() throws IOException {
        return input.nextLine();
    }

    private static int readInt() throws IOException {
        return input.nextInt();
    }

    private static void swap(int[] data, int i, int j) {
        int temp = data[i];
        data[i] = data[j];
        data[j] = temp;
    }

    private static void openConsole() {
        input = new FastScanner(System.in);
        output = new PrintWriter(System.out);
    }

    private static void openFile() throws FileNotFoundException {
        ClassLoader classLoader = Main.class.getClassLoader();
        File myFile = new File(classLoader.getResource("input.txt").getFile());
        input = new FastScanner(new FileInputStream(myFile));
        output = new PrintWriter(System.out);
    }

    private static void closeReader() {
        output.flush();
        output.close();
    }

    static class Pair {
        int id, count;

        Pair(Integer id, Integer count) {
            this.id = id;
            this.count = count;
        }
    }

    static class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        private String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

        boolean hasNext() throws IOException {
            return br.ready() || (st != null && st.hasMoreTokens());
        }

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

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

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        boolean hasNextLine() throws IOException {
            return br.ready();
        }
    }
}