After the piece of a devilish mirror hit the Kay's eye, he is no longer interested in the beauty of the roses. Now he likes to watch snowflakes.

Once upon a time, he found a huge snowflake that has a form of the tree (connected acyclic graph) consisting of n nodes. The root of tree has index 1. Kay is very interested in the structure of this tree.

After doing some research he formed q queries he is interested in. The i-th query asks to find a centroid of the subtree of the node vi. Your goal is to answer all queries.

Subtree of a node is a part of tree consisting of this node and all it's descendants (direct or not). In other words, subtree of node v is formed by nodes u, such that node v is present on the path from u to root.

Centroid of a tree (or a subtree) is a node, such that if we erase it from the tree, the maximum size of the connected component will be at least two times smaller than the size of the initial tree (or a subtree).

Input

The first line of the input contains two integers n and q (2 ≤ n ≤ 300 000, 1 ≤ q ≤ 300 000) — the size of the initial tree and the number of queries respectively.

The second line contains n - 1 integer p2, p3, ..., pn (1 ≤ pi ≤ n) — the indices of the parents of the nodes from 2 to n. Node 1 is a root of the tree. It's guaranteed that pi define a correct tree.

Each of the following q lines contain a single integer vi (1 ≤ vi ≤ n) — the index of the node, that define the subtree, for which we want to find a centroid.

Output

For each query print the index of a centroid of the corresponding subtree. If there are many suitable nodes, print any of them. It's guaranteed, that each subtree has at least one centroid.

Example

Input

7 4
1 1 3 3 5 3
1
2
3
5


Output

3
2
3
6

Note

<image>

The first query asks for a centroid of the whole tree — this is node 3. If we delete node 3 the tree will split in four components, two of size 1 and two of size 2.

The subtree of the second node consists of this node only, so the answer is 2.

Node 3 is centroid of its own subtree.

The centroids of the subtree of the node 5 are nodes 5 and 6 — both answers are considered correct.
import java.io.*;
import java.math.*;
import java.util.*;

public class Main {

	static int mod = (int) 1e9 + 7;
	static int MAX = (int) 1e9;
	static ArrayList<Integer>[] next;
	static int[] size;
	static ArrayList<ArrayList<Integer>> chainsMax;
	static ArrayList<ArrayList<Integer>> chainsVal;
	static int[] pos1;
	static int[] pos2;

	public static void main(String[] args) {
		FasterScanner s = new FasterScanner();
		PrintWriter out = new PrintWriter(System.out);

		int test = 1;// s.nextInt();

		testloop: while (test-- > 0) {
			int n = s.nextInt();
			next = new ArrayList[n];
			int q = s.nextInt();
			for (int i = 0; i < n; i++)
				next[i] = new ArrayList<>();
			for (int i = 1; i < n; i++) {
				next[s.nextInt() - 1].add(i);
			}
			size = new int[n];
			chainsMax = new ArrayList<>();
			chainsVal = new ArrayList<>();
			pos1 = new int[n];
			pos2 = new int[n];
			computeSize(0);
			createChains(0);
			// System.out.println(Arrays.toString(size));
//			System.out.println(chainsVal);
//			System.out.println(chainsMax);
			while (q-- > 0) {
				int u = s.nextInt() - 1;
				ArrayList<Integer> chain = chainsMax.get(pos1[u]);
				int left = 0;
				int right = pos2[u];
				double xx = size[u];
				while (left < right) {
					int mid = (left + right + 1) >> 1;
					if (chain.get(mid) <= xx / 2) {
						left = mid;
					} else {
						right = mid - 1;
					}
				}
				out.println(chainsVal.get(pos1[u]).get(left));
			}
		}
		out.close();
	}

	static int computeSize(int i) {
		int ans = 1;
		for (int v : next[i])
			ans += computeSize(v);
		return (size[i] = ans);
	}

	static void createChains(int u) {
		if (next[u].size() == 0) {
			ArrayList<Integer> chain = new ArrayList<>();
			ArrayList<Integer> chainValue = new ArrayList<>();
			chain.add(0);
			chainValue.add(u + 1);
			pos1[u] = chainsMax.size();
			pos2[u] = 0;
			chainsMax.add(chain);
			chainsVal.add(chainValue);
			return;
		}

		int max = 0, maxindex = 0;
		for (int i = 0; i < next[u].size(); i++) {
			createChains(next[u].get(i));
			if (max < size[next[u].get(i)]) {
				max = size[next[u].get(i)];
				maxindex = next[u].get(i);
			}
		}
		pos1[u] = pos1[maxindex];
		pos2[u] = pos2[maxindex] + 1;
		chainsMax.get(pos1[maxindex]).add(max);
		chainsVal.get(pos1[maxindex]).add(u + 1);
		// System.out.println(u+" "+chainsVal);
	}

	public static class Node implements Comparable<Node> {
		long val;
		int index;

		Node(long val, int index) {
			this.val = val;
			this.index = index;
		}

		@Override
		public int compareTo(Node o) {
			if (this.val != o.val)
				return Long.compare(val, o.val);
			else
				return Integer.compare(this.index, o.index);
		}
	}

	public static int find(int[] a, int val) {
		int left = 0;
		if (val > a[a.length - 1])
			return a.length;
		int right = a.length;

		while (left < right) {

			int mid = (left + right) >> 1;
			// System.out.println("HERE" + left +" " + right +" "+mid);

			if (a[mid] > val) {
				right = mid;
			} else {
				left = mid + 1;
			}
		}
		return right;
	}

	public static void addInTable(Hashtable<Integer, Integer> table, int pos, int val) {
		if (!table.containsKey(pos)) {
			table.put(pos, val);
		} else {
			table.put(pos, table.get(pos) + val);
		}
	}

	static class Player implements Comparable<Player> {
		String name;
		int score;

		Player(String n, int v) {
			name = n;
			score = v;
		}

		@Override
		public int compareTo(Player o) {
			return o.score - score;
		}
	}

	static class Edge {
		int t, rev, f;
		long cap;

		public Edge(int t, int rev, long cap) {
			this.t = t;
			this.rev = rev;
			this.cap = cap;
		}
	}

	public static List<Edge>[] createGraph(int nodes) {
		List<Edge>[] graph = new List[nodes];
		for (int i = 0; i < nodes; i++)
			graph[i] = new ArrayList<>();
		return graph;
	}

	public static void addEdge(List<Edge>[] graph, int s, int t, long cap) {
		graph[s].add(new Edge(t, graph[t].size(), cap));
		graph[t].add(new Edge(s, graph[s].size() - 1, 0));
	}

	static boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
		Arrays.fill(dist, -1);
		dist[src] = 0;
		int[] Q = new int[graph.length];
		int sizeQ = 0;
		Q[sizeQ++] = src;
		for (int i = 0; i < sizeQ; i++) {
			int u = Q[i];
			for (Edge e : graph[u]) {
				if (dist[e.t] < 0 && e.f < e.cap) {
					dist[e.t] = dist[u] + 1;
					Q[sizeQ++] = e.t;
				}
			}
		}
		return dist[dest] >= 0;
	}

	static long dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, long l) {
		if (u == dest)
			return l;
		for (; ptr[u] < graph[u].size(); ++ptr[u]) {
			Edge e = graph[u].get(ptr[u]);
			if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
				long df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(l, e.cap - e.f));
				if (df > 0) {
					e.f += df;
					graph[e.t].get(e.rev).f -= df;
					return df;
				}
			}
		}
		return 0;
	}

	public static long maxFlow(List<Edge>[] graph, int src, int dest) {
		long flow = 0;
		int[] dist = new int[graph.length];
		while (dinicBfs(graph, src, dest, dist)) {
			int[] ptr = new int[graph.length];
			while (true) {
				long df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
				if (df == 0)
					break;
				flow += df;
			}
		}
		return flow;
	}

	static int ans(ArrayList<Character>[] l, char a, int n) {
		if (n == 1)
			return 1;
		int sum = 0;
		for (int i = 0; i < l[a - 'a'].size(); i++) {
			sum += ans(l, l[a - 'a'].get(i), n - 1);
		}
		return sum;
	}

	static void dfs1(List<Integer>[] graph, boolean[] used, List<Integer> order, int u) {
		used[u] = true;
		for (int v : graph[u])
			if (!used[v])
				dfs1(graph, used, order, v);
		order.add(u);
	}

	static void dfs2(List<Integer>[] reverseGraph, int[] comp, int u, int color) {
		comp[u] = color;
		for (int v : reverseGraph[u])
			if (comp[v] == -1)
				dfs2(reverseGraph, comp, v, color);
	}

	public static boolean[] solve2Sat(List<Integer>[] graph) {
		int n = graph.length;
		boolean[] used = new boolean[n];
		List<Integer> order = new ArrayList<>();
		for (int i = 0; i < n; ++i)
			if (!used[i])
				dfs1(graph, used, order, i);

		List<Integer>[] reverseGraph = new List[n];
		for (int i = 0; i < n; i++)
			reverseGraph[i] = new ArrayList<>();
		for (int i = 0; i < n; i++)
			for (int j : graph[i])
				reverseGraph[j].add(i);

		int[] comp = new int[n];
		Arrays.fill(comp, -1);
		for (int i = 0, color = 0; i < n; ++i) {
			int u = order.get(n - i - 1);
			if (comp[u] == -1)
				dfs2(reverseGraph, comp, u, color++);
		}

		for (int i = 0; i < n; ++i)
			if (comp[i] == comp[i ^ 1])
				return null;

		boolean[] res = new boolean[n / 2];
		for (int i = 0; i < n; i += 2)
			res[i / 2] = comp[i] > comp[i ^ 1];
		return res;
	}

	public static int[] createSets(int size) {
		int[] p = new int[size];
		for (int i = 0; i < size; i++)
			p[i] = i;
		return p;
	}

	public static int root(int[] p, int x) {
		return x == p[x] ? x : (p[x] = root(p, p[x]));
	}

	public static void unite(int[] p, int a, int b) {
		a = root(p, a);
		b = root(p, b);
		if (a != b)
			p[a] = b;
	}

	public static boolean nextPermutation(int[] p) {
		for (int a = p.length - 2; a >= 0; --a)
			if (p[a] < p[a + 1])
				for (int b = p.length - 1;; --b)
					if (p[b] > p[a]) {
						int t = p[a];
						p[a] = p[b];
						p[b] = t;
						for (++a, b = p.length - 1; a < b; ++a, --b) {
							t = p[a];
							p[a] = p[b];
							p[b] = t;
						}
						return true;
					}
		return false;
	}

	public static boolean isPrime(long n) {
		if (n <= 1)
			return false;
		for (long i = 2; i * i <= n; i++)
			if (n % i == 0)
				return false;
		return true;
	}

	static class SegTree {
		int[] val;
		int n;

		SegTree(int n) {
			val = new int[2 * n];
			this.n = n;
		}

		void upd(int p, int l) {
			p += n;
			val[p] = l;
			for (; (p >>= 1) != 0;) {
				val[p] = Math.max(val[2 * p], val[2 * p + 1]);

			}
		}

		int query(int l, int r) { // sum on interval [l, r)
			// System.out.println(l+" "+r);
			int res = 0;
			for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
				if ((l & 1) != 0)
					res = Math.max(res, val[l++]);
				if ((r & 1) != 0)
					res = Math.max(res, val[--r]);
			}
			return res;
		}
	}

	static boolean check(int i, int j, int n) {
		if (i >= 0 && j >= 0 && i < n && j < n)
			return true;
		return false;
	}

	public static int[] generateDivisorTable(int n) {
		int[] divisor = new int[n + 1];
		for (int i = 1; i <= n; i++)
			divisor[i] = i;
		for (int i = 2; i * i <= n; i++)
			if (divisor[i] == i)
				for (int j = i * i; j <= n; j += i)
					divisor[j] = i;
		return divisor;
	}

	public static int[][] matrixMul(int[][] a, int[][] b) {
		int n = a.length;
		int m = a[0].length;
		int k = b[0].length;
		int[][] res = new int[n][k];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < k; j++) {
				for (int p = 0; p < m; p++) {
					res[i][j] = (res[i][j] + (int) ((a[i][p] * 1l * b[p][j]) % mod)) % mod;
				}
			}
		}
		return res;
	}

	public static int[][] matrixPow(int[][] a, int p) {
		if (p == 0) {
			return matrixUnit(a.length);
		} else if (p % 2 == 0) {
			return matrixPow(matrixMul(a, a), p / 2);
		} else {
			return matrixMul(a, matrixPow(a, p - 1));
		}
	}

	public static int[][] matrixUnit(int n) {
		int[][] res = new int[n][n];
		for (int i = 0; i < n; ++i) {
			res[i][i] = 1;
		}
		return res;
	}

	static int[] modInv(int n, int mod) {
		int[] ans = new int[n];
		for (int i = 1; i < n; i++)
			ans[i] = (int) pow(i, mod - 2, mod);
		return ans;
	}

	static int[] primes;

	public static long ncr(int n, int r) {
		if (n < r)
			return 0;
		if (n == r)
			return 1;
		if (r == 0)
			return 1;
		if (r < 0)
			return 0;
		long ans = 1;
		for (int i = 0; i < primes.length; i++) {
			long power = count(n, primes[i]) - count(n - r, primes[i]) - count(r, primes[i]);
			ans *= pow(primes[i], power, mod);
			ans %= mod;
		}
		return ans;
	}

	public static long pow(long x, long n, int mod) {
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
			if ((n & 1) != 0) {
				res = (int) (res * p % mod);
			}
		}
		return res;
	}

	public static long count(int n, int p) {
		long count = 0;
		long z = p;
		while (z <= n) {
			count += n / z;
			z *= p;
		}
		return count;

	}

	public static int[] generatePrimes(int n) {
		boolean[] prime = new boolean[n + 1];
		Arrays.fill(prime, 2, n + 1, true);
		for (int i = 2; i * i <= n; i++)
			if (prime[i])
				for (int j = i * i; j <= n; j += i)
					prime[j] = false;
		int[] primes = new int[n + 1];
		int cnt = 0;
		for (int i = 0; i < prime.length; i++)
			if (prime[i])
				primes[cnt++] = i;

		return Arrays.copyOf(primes, cnt);
	}

	static class Pairxy implements Comparable<Pairxy> {
		int x;
		int y;

		Pairxy(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(Pairxy o) {
			return Integer.compare(this.x, o.x);
		}

	}

	public static long C(int n, int r) {
		long ans = 1;
		int x = 1;
		while (x <= r) {
			ans *= n;
			ans /= x;
			x++;
			n--;
		}
		return ans;
	}

	static class DisjointSetsRank {

		int[] p;
		int[] rank;
		int[] size;

		public DisjointSetsRank(int size) {
			p = new int[size];
			this.size = new int[size];
			for (int i = 0; i < size; i++) {
				p[i] = i;
				this.size[i] = 1;
			}
			rank = new int[size];
		}

		public int root(int x) {
			return x == p[x] ? x : (p[x] = root(p[x]));
		}

		public int sameSet(int x, int y) {
			if (root(x) == root(y))
				return 1;
			return 0;

		}

		public int unite(int a, int b) {
			a = root(a);
			b = root(b);
			if (a == b)
				return -1;

			if (rank[a] < rank[b]) {
				p[a] = b;
				size[b] += size[a];
				return a;
			} else {
				p[b] = a;
				size[a] += size[b];
				if (rank[a] == rank[b])
					++rank[a];
				return b;
			}
		}

	}

	static int gcd(long m, long n) {
		long x;
		long y;
		while (m % n != 0) {
			x = n;
			y = m % n;
			m = x;
			n = y;
		}
		return (int) n;
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}
