Xenia the programmer has a tree consisting of n nodes. We will consider the tree nodes indexed from 1 to n. We will also consider the first node to be initially painted red, and the other nodes — to be painted blue.

The distance between two tree nodes v and u is the number of edges in the shortest path between v and u.

Xenia needs to learn how to quickly execute queries of two types:

  1. paint a specified blue node in red; 
  2. calculate which red node is the closest to the given one and print the shortest distance to the closest red node. 



Your task is to write a program which will execute the described queries.

Input

The first line contains two integers n and m (2 ≤ n ≤ 105, 1 ≤ m ≤ 105) — the number of nodes in the tree and the number of queries. Next n - 1 lines contain the tree edges, the i-th line contains a pair of integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi) — an edge of the tree.

Next m lines contain queries. Each query is specified as a pair of integers ti, vi (1 ≤ ti ≤ 2, 1 ≤ vi ≤ n). If ti = 1, then as a reply to the query we need to paint a blue node vi in red. If ti = 2, then we should reply to the query by printing the shortest distance from some red node to node vi.

It is guaranteed that the given graph is a tree and that all queries are correct.

Output

For each second type query print the reply in a single line.

Examples

Input

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


Output

0
3
2
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve() {
		int n = ni(), m = ni();
		int[] from = new int[n-1];
		int[] to = new int[n-1];
		for(int i = 0; i < n-1; i++) {
			from[i] = ni()-1;
			to[i] = ni()-1;
		}
		int[][] g = packU(n, from, to);
		int[][] pars = parents3(g, 0);
		int[] par = pars[0], dep = pars[2];
		int[][] spar = logstepParents(par);
		int[] cpar = buildCentroidTree(g);
		int[] ans = new int[n];
		Arrays.fill(ans, Integer.MAX_VALUE / 2);
		update(0, cpar, ans, spar, dep);
		for(int q = 0; q < m; q++) {
			int t = ni();
			if(t == 1) {
				int u = ni()-1;
				update(u, cpar, ans, spar, dep);
			}
			else {
				int u = ni()-1;
				out.println(query(u, cpar, ans, spar, dep));
			}
		}
	}
	
	public int query(int u, int[] cpar, int[] ans, int[][] spar, int[] dep) {
		int min = ans[u];
		int par = cpar[u];
		while(par != -1) {
			min = Math.min(min, d(u, par, spar, dep) + ans[par]);
			par = cpar[par];
		}
		return min;
	}
	
	public void update(int u, int[] cpar, int[] ans, int[][] spar, int[] dep) {
		ans[u] = 0;
		int par = cpar[u];
		while(par != -1) {
			ans[par] = Math.min(ans[par], d(u, par, spar, dep));
			par = cpar[par];
		}
	}
	
	public static int[] buildCentroidTree(int[][] g) {
		int n = g.length;
		int[] ctpar = new int[n];
		Arrays.fill(ctpar, -1);
		buildCentroidTree(g, 0, new boolean[n], new int[n], new int[n], new int[n], ctpar);
		return ctpar;
	}
	
	private static int buildCentroidTree(int[][] g, int root, boolean[] sed, int[] par, int[] ord, int[] des, int[] ctpar)
	{
		// parent and level-order
		ord[0] = root;
		par[root] = -1;
		int r = 1;
		for(int p = 0;p < r;p++) {
			int cur = ord[p];
			for(int nex : g[cur]){
				if(par[cur] != nex && !sed[nex]){
					ord[r++] = nex;
					par[nex] = cur;
				}
			}
		}
		// if(r == 1)return;
		
		// DP and find a separator
		int sep = -1; // always exists
		outer:
		for(int i = r-1;i >= 0;i--){
			int cur = ord[i];
			des[cur] = 1;
			for(int e : g[cur]){
				if(par[cur] != e && !sed[e])des[cur] += des[e];
			}
			if(r-des[cur] <= r/2){
				for(int e : g[cur]){
					if(par[cur] != e && !sed[e] && des[e] >= r/2+1)continue outer;
				}
				sep = cur;
				break;
			}
		}
		
		sed[sep] = true;
		for(int e : g[sep]){
			if(!sed[e])ctpar[buildCentroidTree(g, e, sed, par, ord, des, ctpar)] = sep;
		}
		return sep;
	}
	
	public static int lca2(int a, int b, int[][] spar, int[] depth)
	{
		if(depth[a] < depth[b]){
			b = ancestor(b, depth[b]-depth[a], spar);
		}else if(depth[a] > depth[b]){
			a = ancestor(a, depth[a]-depth[b], spar);
		}
		
		if(a == b)return a;
		int sa = a, sb = b;
		for(int low = 0, high = depth[a], t = Integer.highestOneBit(high), k = Integer.numberOfTrailingZeros(t);t > 0;t>>>=1,k--){
			if((low^high) >= t){
				if(spar[k][sa] != spar[k][sb]){
					low |= t;
					sa = spar[k][sa]; sb = spar[k][sb];
				}else{
					high = low|t-1;
				}
			}
		}
		return spar[0][sa];
	}
	
	protected static int ancestor(int a, int m, int[][] spar)
	{
		for(int i = 0;m > 0 && a != -1;m>>>=1,i++){
			if((m&1)==1)a = spar[i][a];
		}
		return a;
	}
	
	public static int[][] logstepParents(int[] par)
	{
		int n = par.length;
		int m = Integer.numberOfTrailingZeros(Integer.highestOneBit(n-1))+1;
		int[][] pars = new int[m][n];
		pars[0] = par;
		for(int j = 1;j < m;j++){
			for(int i = 0;i < n;i++){
				pars[j][i] = pars[j-1][i] == -1 ? -1 : pars[j-1][pars[j-1][i]];
			}
		}
		return pars;
	}
	
	public int d(int u, int v, int[][] spar, int[] dep) {
		return dep[u] + dep[v] - 2 *dep[lca2(u, v, spar, dep)];
	}
	

	public static int[][] parents3(int[][] g, int root)
	{
		int n = g.length;
		int[] par = new int[n];
		Arrays.fill(par, -1);
		
		int[] depth = new int[n];
		depth[0] = 0;
		
		int[] q = new int[n];
		q[0] = root;
		for(int p = 0, r = 1;p < r;p++) {
			int cur = q[p];
			for(int nex : g[cur]){
				if(par[cur] != nex){
					q[r++] = nex;
					par[nex] = cur;
					depth[nex] = depth[cur] + 1;
				}
			}
		}
		return new int[][] {par, q, depth};
	}
	
	static int[][] packU(int n, int[] from, int[] to) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for(int f : from)
			p[f]++;
		for(int t : to)
			p[t]++;
		for(int i = 0;i < n;i++)
			g[i] = new int[p[i]];
		for(int i = 0;i < from.length;i++){
			g[from[i]][--p[from[i]]] = to[i];
			g[to[i]][--p[to[i]]] = from[i];
		}
		return g;
	}
			
	void run() throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);

		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if (!INPUT.isEmpty())
			tr(System.currentTimeMillis() - s + "ms");
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

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

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

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

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}

	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private int ni() {
		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();
		}
	}

	private long nl() {
		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();
		}
	}

	private static void tr(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
}