Roman planted a tree consisting of n vertices. Each vertex contains a lowercase English letter. Vertex 1 is the root of the tree, each of the n - 1 remaining vertices has a parent in the tree. Vertex is connected with its parent by an edge. The parent of vertex i is vertex pi, the parent index is always less than the index of the vertex (i.e., pi < i).

The depth of the vertex is the number of nodes on the path from the root to v along the edges. In particular, the depth of the root is equal to 1.

We say that vertex u is in the subtree of vertex v, if we can get from u to v, moving from the vertex to the parent. In particular, vertex v is in its subtree.

Roma gives you m queries, the i-th of which consists of two numbers vi, hi. Let's consider the vertices in the subtree vi located at depth hi. Determine whether you can use the letters written at these vertices to make a string that is a palindrome. The letters that are written in the vertexes, can be rearranged in any order to make a palindrome, but all letters should be used.

Input

The first line contains two integers n, m (1 ≤ n, m ≤ 500 000) — the number of nodes in the tree and queries, respectively.

The following line contains n - 1 integers p2, p3, ..., pn — the parents of vertices from the second to the n-th (1 ≤ pi < i).

The next line contains n lowercase English letters, the i-th of these letters is written on vertex i.

Next m lines describe the queries, the i-th line contains two numbers vi, hi (1 ≤ vi, hi ≤ n) — the vertex and the depth that appear in the i-th query.

Output

Print m lines. In the i-th line print "Yes" (without the quotes), if in the i-th query you can make a palindrome from the letters written on the vertices, otherwise print "No" (without the quotes).

Examples

Input

6 5
1 1 1 3 3
zacccd
1 1
3 3
4 1
6 1
1 2


Output

Yes
No
Yes
Yes
Yes

Note

String s is a palindrome if reads the same from left to right and from right to left. In particular, an empty string is a palindrome.

Clarification for the sample test.

In the first query there exists only a vertex 1 satisfying all the conditions, we can form a palindrome "z".

In the second query vertices 5 and 6 satisfy condititions, they contain letters "с" and "d" respectively. It is impossible to form a palindrome of them.

In the third query there exist no vertices at depth 1 and in subtree of 4. We may form an empty palindrome.

In the fourth query there exist no vertices in subtree of 6 at depth 1. We may form an empty palindrome.

In the fifth query there vertices 2, 3 and 4 satisfying all conditions above, they contain letters "a", "c" and "c". We may form a palindrome "cac".
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    static boolean isMultiTest = false;

    public static void main(String[] args) {
        OutputStream outputStream = System.out;
        InputStream inputStream = System.in;
        InputFast in = new InputFast();
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        if (isMultiTest) {
            int testNumber = in.nextInt();
            for (int i = 1; i <= testNumber; i++) {
                solver.solve(i, in, out);
            }
        } else {
            solver.solve(1, in, out);
        }
        out.close();
    }
}

class Task {
    final static int MOD = 1000 * 1000 * 1000 + 7;
    char[] valueChars;
    List<Integer>[] childs;
    int[] starts;
    int[] ends;
    int[] masks;
    int index = -1;
    TreeSet<Pair>[] set;

    public void solve(int testNumber, InputFast in, PrintWriter out) {
        int nVertices = in.nextInt();
        int nQueries = in.nextInt();

        childs = new List[nVertices];
        set = new TreeSet[nVertices];

        masks = new int[26];
        for (int i = 0; i < 26; i++) {
            masks[i] = 1 << i;
        }

        for (int i = 0; i < nVertices; i++) {
            childs[i] = new ArrayList<Integer>();
            set[i] = new TreeSet<Pair>();
        }

        for (int i = 1; i < nVertices; i++) {
            int parent = in.nextInt() - 1;
            childs[parent].add(i);
        }

        starts = new int[nVertices];
        ends = new int[nVertices];
        valueChars = in.next().toCharArray();

        dfs(0, 0);

        for (int i = 0; i < nQueries; i++) {
            int root = in.nextInt() - 1;
            int depth = in.nextInt() - 1;

            Pair left = set[depth].lower(new Pair(starts[root], -1));
            Pair right = set[depth].lower(new Pair(ends[root] + 1, -1));
            if (right == null) {
                out.println("Yes");
                continue;
            }
            if (right.first < starts[root]) {
                out.println("Yes");
                continue;
            }
            int count = 0;
            int v = right.second;
            if (left != null)
                v ^= left.second;

            if (Integer.bitCount(v) <= 1) {
                out.println("Yes");
            } else {
                out.println("No");
            }
        }
    }

    private void dfs(int root, int depth) {
        starts[root] = ++index;
        int second = set[depth].size() == 0 ? 0 : set[depth].last().second;
        set[depth].add(new Pair(index, second ^ masks[valueChars[root] - 'a']));
        for (int child : childs[root]) {
            dfs(child, depth + 1);
        }
        ends[root] = index;

    }

    class Pair implements Comparable<Pair> {
        int first;
        int second;

        public Pair(int f, int s) {
            this.first = f;
            this.second = s;
        }

        @Override
        public int compareTo(Pair p) {
            return this.first - p.first;
        }
    }
}

class InputFast {
    static InputStream is = System.in;
    static private byte[] buffer = new byte[1024];
    static private int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1)
            throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(buffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0)
                return -1;
        }
        return buffer[ptrbuf++];
    }

    private boolean isSpace(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int read() {
        int b;
        while ((b = readByte()) != -1 && isSpace(b))
            ;
        return b;
    }

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

    public char nextChar() {
        return (char) read();
    }

    public String next() {
        int b = read();
        StringBuilder sb = new StringBuilder();
        while (!(isSpace(b))) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public char[] next(int n) {
        char[] buf = new char[n];
        int b = read(), p = 0;
        while (p < n && !(isSpace(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    public int nextInt() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
            ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    public long nextLong() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
            ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

}

class Input {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public Input(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        String s = "";
        try {
            s = reader.readLine();
        } catch (IOException e) {
            try {
                throw new IOException();
            } catch (IOException e1) {
                e1.printStackTrace();
            }
        }
        return s;
    }

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

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

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