Problem:
Problem F: Marked Ancestor

You are given a tree T that consists of N nodes. Each node is numbered from 1 to N, and node 1 is always the root node of T. Consider the following two operations on T:

M v: (Mark) Mark node v.

Q v: (Query) Print the index of the nearest marked ancestor of node v which is nearest to it. Initially, only the root node is marked. Note that a node is an ancestor of itself.

Your job is to write a program that performs a sequence of these operations on a given tree and calculates
the value that each Q operation will print. To avoid too large output file, your program is requested to
print the sum of the outputs of all query operations. Note that the judges confirmed that it is possible to
calculate every output of query operations in a given sequence.

Input

The input consists of multiple datasets. Each dataset has the following format:

The first line of the input contains two integers N and Q, which denotes the number of nodes in the tree
T and the number of operations, respectively. These numbers meet the following conditions: 1 ≤ N ≤ 100000 and 1 ≤ Q ≤ 100000.

The following N - 1 lines describe the configuration of the tree T. Each line contains a single integer pi (i = 2, ... , N), which represents the index of the parent of i-th node.

The next Q lines contain operations in order. Each operation is formatted as "M v" or "Q v", where v is the index of a node.

The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.

Output

For each dataset, print the sum of the outputs of all query operations in one line.

Sample Input

6 3
1
1
2
3
3
Q 5
M 3
Q 5
0 0

Output for the Sample Input

4

Solution in JAVA (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main implements Runnable {
	static IO io = new IO();
	public static void main(String[] args) {
		new Thread(null, new Main(), "", 1024L * 1024 * 48).start();
	}
	
	public void run() {
		while(solve());
		io.flush();
	}
	
	int n;
	int q;
	int[] parent;
	ArrayList<Integer>[] child;
	boolean[] marked;
	int[] ma;
	ArrayDeque<Integer> stack;
	
	@SuppressWarnings("unchecked")
	public boolean solve() {
		n = io.nextInt();
		q = io.nextInt();
		if (n == 0) {
			return false;
		}
		child = new ArrayList[n];
		parent = new int[n];
		parent[0] = -1;
		for(int i=0;i<n;i++) {
			child[i] = new ArrayList<>();
		}
		for(int i=0;i<n-1;i++) {
			int p = io.nextInt() - 1;
			parent[i] = p;
			child[p].add(i+1);
		}
		char[] qType = new char[q];
		int[] qVal = new int[q];
		for(int i=0;i<q;i++) {
			qType[i] = io.nextChar();
			qVal[i] = io.nextInt() - 1;
		}
		marked = new boolean[n];
		marked[0] = true;
		for(int i=0;i<q;i++) {
			if (qType[i] == 'M') {
				marked[qVal[i]] = true;
			}
		}
		stack = new ArrayDeque<>();
		ma = new int[n];
		dfs(0);
		UnionFind uf = new UnionFind(n);
		for(int i=0;i<n;i++) {
			uf.union(ma[i], i);
		}
		int sum = 0;
		for(int i=q-1;i>=0;i--) {
			if (qType[i] == 'Q') {
				sum += uf.get(qVal[i]) + 1;
			}else{
				if (parent[qVal[i]] >= 0) {
					uf.union(parent[qVal[i]], qVal[i]);
				}
			}
		}
		io.println(sum);
		return true;
	}
	

	public void dfs(int v) {
		if (marked[v]) {
			stack.push(v);
		}
		ma[v] = stack.peek();
		for(int c: child[v]) {
			dfs(c);
		}
		if (marked[v]) {
			stack.pop();
		}
	}

}
class UnionFind {
	private int[] parent;
	private int[] data;
	public UnionFind(int size) {
		parent = new int[size];
		data = new int[size];
		for(int i=0;i<size;i++) {
			data[i] = i;
		}
		Arrays.fill(parent, -1);
	}
	public boolean union(int x,int y) {
		x = root(x);
		y = root(y);
		if (x!=y) {
			int nData = data[x];
			if (parent[y] < parent[x]) {
				int tmp = y;
				y = x;
				x = tmp;
			}
			data[x] = nData;
			parent[x] += parent[y];
			parent[y] = x;
			return true;
		}
		return false;
	}
	public boolean isConnected(int x,int y) {
		return root(x)==root(y);
	}
	private int root(int x) {
		return parent[x] < 0 ? x : (parent[x] = root(parent[x]));
	}
	public int size(int x) {
		return -parent[root(x)];
	}
	public int get(int x) {
		return data[root(x)];
	}
	public ArrayList<ArrayList<Integer>> groups() {
		int n = parent.length;
		ArrayList<ArrayList<Integer>> g = new ArrayList<ArrayList<Integer>>();
		HashMap<Integer,Integer> hm = new HashMap<Integer, Integer>();
		for(int i=0;i<n;i++) {
			int r = root(i);
			if (!hm.containsKey(r)) {
				hm.put(r, g.size());
				g.add(new ArrayList<Integer>());
			}
			g.get(hm.get(r)).add(i);
		}
		return g;
	}
	public String toString() {
		return Arrays.toString(parent);
	}
}
class IO extends PrintWriter {
	private final InputStream in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	
	public IO() { this(System.in);}
	public IO(InputStream source) { super(System.out); this.in = source;}
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	private static boolean isNewLine(int c) { return c == '\n' || c == '\r';}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public boolean hasNextLine() { while(hasNextByte() && isNewLine(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public char[] nextCharArray(int len) {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		char[] s = new char[len];
		int i = 0;
		int b = readByte();
		while(isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}
	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(!isNewLine(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}
	public double nextDouble() { return Double.parseDouble(next());}
	public int[] nextIntArray(int n) { int[] a = new int[n]; for(int i=0;i<n;i++) a[i] = nextInt(); return a;}
	public long[] nextLongArray(int n) { long[] a = new long[n]; for(int i=0;i<n;i++) a[i] = nextLong(); return a;}
	public double[] nextDoubleArray(int n) { double[] a = new double[n]; for(int i=0;i<n;i++) a[i] = nextDouble(); return a;}
	public void nextIntArrays(int[]... a) { for(int i=0;i<a[0].length;i++) for(int j=0;j<a.length;j++) a[j][i] = nextInt();}
	public int[][] nextIntMatrix(int n,int m) { int[][] a = new int[n][]; for(int i=0;i<n;i++) a[i] = nextIntArray(m); return a;}
	public char[][] nextCharMap(int n,int m) { char[][] a = new char[n][]; for(int i=0;i<n;i++) a[i] = nextCharArray(m); return a;}
	public void close() { super.close(); try {in.close();} catch (IOException e) {}}
}