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:
// Main Code at the Bottom
import java.util.*;
import java.io.*; 
public class Main implements Runnable{
	//Fast IO class
    static class FastReader {
        BufferedReader br; 
        StringTokenizer st; 
        public FastReader() {
        	boolean env=System.getProperty("ONLINE_JUDGE") != null;
        	//env=true;
        	if(!env) {
        		try {
					br=new BufferedReader(new FileReader("src\\input.txt"));
				} catch (FileNotFoundException e) {
					e.printStackTrace();
				}
        	}
        	else br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) {
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
        int nextInt() {
            return Integer.parseInt(next()); 
        } 
        long nextLong() {
            return Long.parseLong(next()); 
        } 
        double nextDouble() {
            return Double.parseDouble(next()); 
        } 
        String nextLine() {
            String str = ""; 
            try {
                str = br.readLine(); 
            } 
            catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }     
    static long MOD=(long)1e9+7;
    //debug
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
    static FastReader sc=new FastReader();
    static PrintWriter out=new PrintWriter(System.out);  
    //Global variables and functions
    HashSet<Integer> x, y, visited, cur;
    int ans[];
    int V;
    ArrayList<Integer> graph[];
    void init(int n) {
    	V = n;
    	 x= new HashSet<>();
    	 y = new HashSet<>();
    	 graph = new ArrayList[V];
    	 visited = new HashSet<>();
    	 for(int i = 0; i < V; i++) {
    		 graph[i] = new ArrayList<>();
    	 }
    }
    void addEdge(int src, int dest) {
    	graph[src].add(dest);
    }
    void dfs1(int s) {
    	if(cur.contains(s)) {
    		y.add(s);
    		return;
    	}
    	if(visited.contains(s)) {
    		x.add(s);
    		return;
    	}
    	ans[s] = 1;
    	visited.add(s);
    	cur.add(s);
    	for(Integer v: graph[s]) {
    		dfs1(v);
    	}
    	cur.remove(s);
    }
    void dfs2(int s, int val) {
    	if(visited.contains(s)) {
    		return;
    	}
    	visited.add(s);
    	ans[s] = val;
    	for(Integer v: graph[s]) {
    		dfs2(v, val);
    	}
    }
    //Main function(The main code starts from here)
    public void run() {
    	int test=1;
    	test=sc.nextInt();
    	while(test-->0) {
    		int n = sc.nextInt(), m = sc.nextInt();
    		init(n);
    		while(m-- > 0) {
    			addEdge(sc.nextInt() - 1, sc.nextInt() - 1);
    		}
    		cur = new HashSet<>();
    		ans = new int[n];
    		dfs1(0);
    		visited.clear();
    		for(int u: x) dfs2(u, 2);
    		visited.clear();
    		for(int u: y) dfs2(u, -1);
    		for(int i: ans) {
    			out.print(i+" ");
    		}
    		out.println();
    		

    	}
        out.flush();
        out.close();
    }
    public static void main (String[] args) throws java.lang.Exception {
    	new Thread(null, new Main(), "anything", (1<<28)).start();
    }
}