Problem: You are given a directed graph G which can contain loops (edges from a vertex to itself). Multi-edges are absent in G which means that for all ordered pairs (u, v) exists at most one edge from u to v. Vertices are numbered from 1 to n.

A path from u to v is a sequence of edges such that:

  * vertex u is the start of the first edge in the path; 
  * vertex v is the end of the last edge in the path; 
  * for all pairs of adjacent edges next edge starts at the vertex that the previous edge ends on. 



We will assume that the empty sequence of edges is a path from u to u.

For each vertex v output one of four values:

  * 0, if there are no paths from 1 to v; 
  * 1, if there is only one path from 1 to v; 
  * 2, if there is more than one path from 1 to v and the number of paths is finite; 
  * -1, if the number of paths from 1 to v is infinite. 



Let's look at the example shown in the figure.

<image>

Then:

  * the answer for vertex 1 is 1: there is only one path from 1 to 1 (path with length 0); 
  * the answer for vertex 2 is 0: there are no paths from 1 to 2; 
  * the answer for vertex 3 is 1: there is only one path from 1 to 3 (it is the edge (1, 3)); 
  * the answer for vertex 4 is 2: there are more than one paths from 1 to 4 and the number of paths are finite (two paths: [(1, 3), (3, 4)] and [(1, 4)]); 
  * the answer for vertex 5 is -1: the number of paths from 1 to 5 is infinite (the loop can be used in a path many times); 
  * the answer for vertex 6 is -1: the number of paths from 1 to 6 is infinite (the loop can be used in a path many times). 

Input

The first contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow. Before each test case, there is an empty line.

The first line of the test case contains two integers n and m (1 ≤ n ≤ 4 ⋅ 10^5, 0 ≤ m ≤ 4 ⋅ 10^5) — numbers of vertices and edges in graph respectively. The next m lines contain edges descriptions. Each line contains two integers a_i, b_i (1 ≤ a_i, b_i ≤ n) — the start and the end of the i-th edge. The vertices of the graph are numbered from 1 to n. The given graph can contain loops (it is possible that a_i = b_i), but cannot contain multi-edges (it is not possible that a_i = a_j and b_i = b_j for i ≠ j).

The sum of n over all test cases does not exceed 4 ⋅ 10^5. Similarly, the sum of m over all test cases does not exceed 4 ⋅ 10^5.

Output

Output t lines. The i-th line should contain an answer for the i-th test case: a sequence of n integers from -1 to 2.

Example

Input


5

6 7
1 4
1 3
3 4
4 5
2 1
5 5
5 6

1 0

3 3
1 2
2 3
3 1

5 0

4 4
1 2
2 3
1 4
4 3


Output


1 0 1 2 -1 -1 
1 
-1 -1 -1 
1 0 0 0 0 
1 1 2 1 

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Random;
import java.util.Stack;
import java.util.ArrayList;
import java.util.Vector;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author sarthakmanna
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        GHowManyPaths solver = new GHowManyPaths();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class GHowManyPaths {
        final static Helper hp = new Helper();
        int N;
        int M;
        ArrayList<Integer>[] graph;
        ArrayList<Integer>[] revGraph;
        boolean[] reachable;
        int[] indegree;
        int[] status;

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int i, j, k;

            N = in.nextInt();
            M = in.nextInt();
            graph = new ArrayList[N];
            revGraph = new ArrayList[N];
            for (i = 0; i < N; ++i) {
                graph[i] = new ArrayList<>();
                revGraph[i] = new ArrayList<>();
            }
            for (i = 0; i < M; ++i) {
                int a = in.nextInt() - 1, b = in.nextInt() - 1;
                graph[a].add(b);
                revGraph[b].add(a);
            }

            status = new int[N];
            reachable = new boolean[N];

            calcIsReachable(0);
            indegree = new int[N];
            for (i = 0; i < N; ++i)
                for (int itr : graph[i]) {
                    if (reachable[i] && reachable[itr]) {
                        if (i == itr) {
                            status[i] = -1;
                        } else {
                            ++indegree[itr];
                        }
                    }
                }

            kosaraju();
            dfs();

            out.println(hp.joinElements(status));
        }

        void kosaraju() {
            Stack<Integer> stack = new Stack<>();
            dfs(0, stack, new boolean[N]);
            boolean[] vis = new boolean[N];

            while (!stack.isEmpty()) {
                int top = stack.pop();
                ArrayList<Integer> connected = new ArrayList<>();
                explore(top, connected, vis);
                if (connected.size() > 1) {
                    for (int itr : connected) status[itr] = -1;
                }
                //System.err.print(connected + ", ");
            }
            //System.err.println();
        }

        void dfs(int node, Stack<Integer> stack, boolean[] vis) {
            if (vis[node]) return;
            vis[node] = true;

            for (int itr : graph[node])
                if (reachable[itr]) {
                    dfs(itr, stack, vis);
                }
            stack.add(node);
        }

        void explore(int node, ArrayList<Integer> scc, boolean[] vis) {
            if (vis[node]) return;
            vis[node] = true;
            scc.add(node);

            for (int itr : revGraph[node])
                if (reachable[itr]) {
                    explore(itr, scc, vis);
                }
        }

        void calcIsReachable(int node) {
            if (reachable[node]) return;
            reachable[node] = true;
            for (int itr : graph[node]) calcIsReachable(itr);
        }

        void dfs() {
            boolean[] vis = new boolean[N];
            ArrayDeque<Integer> queue = new ArrayDeque<>();
            queue.addLast(0);
            if (status[0] == 0) status[0] = 1;

            while (!queue.isEmpty()) {
                int node = queue.pollFirst();
                if (vis[node]) continue;
                vis[node] = true;

                for (int itr : graph[node])
                    if (reachable[itr]) {
                        if (status[itr] == 0 || status[node] == -1) {
                            status[itr] = status[node];
                        } else if (status[itr] == 1) {
                            status[itr] = 2;
                        }

                        if (--indegree[itr] == 0 || status[itr] == -1) {
                            queue.addLast(itr);
                        }
                    }
            }
        }

    }

    static class Helper {
        public final long MOD;
        public final int MAXN;
        final Random rnd;

        public Helper() {
            MOD = 1000_000_007;
            MAXN = 1000_006;
            rnd = new Random();
        }

        public Helper(long mod, int maxn) {
            MOD = mod;
            MAXN = maxn;
            rnd = new Random();
        }

        public String joinElements(int... ar) {
            StringBuilder sb = new StringBuilder();
            for (int itr : ar) sb.append(itr).append(" ");
            return sb.toString().trim();
        }

    }

    static class FastReader {
        static final int BUFSIZE = 1 << 20;
        static byte[] buf;
        static int index;
        static int total;
        static InputStream in;

        public FastReader(InputStream is) {
            try {
                in = is;
                buf = new byte[BUFSIZE];
            } catch (Exception e) {
            }
        }

        private int scan() {
            try {
                if (index >= total) {
                    index = 0;
                    total = in.read(buf);
                    if (total <= 0)
                        return -1;
                }
                return buf[index++];
            } catch (Exception | Error e) {
                System.err.println(e.getMessage());
                return 13 / 0;
            }
        }

        public String next() {
            int c;
            for (c = scan(); c <= 32; c = scan()) ;
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan())
                sb.append((char) c);
            return sb.toString();
        }

        public int nextInt() {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+')
                c = scan();
            for (; c >= '0' && c <= '9'; c = scan())
                val = (val << 3) + (val << 1) + (c & 15);
            return neg ? -val : val;
        }

    }
}