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.util.ArrayList;
import java.util.Scanner;

public class HowManyPaths {
	
	static int[] visited;
	static ArrayList<ArrayList<Integer>> index;
	
	public static void dfs2(ArrayList<ArrayList<Integer>> graph, int current, int val) {
		
		visited[current] = val;
		for (int neighbour : graph.get(current)) {
			if (visited[neighbour] != val) {
				dfs2(graph, neighbour, val);
			}
		}
		
	}
	
	public static void dfs(ArrayList<ArrayList<Integer>> graph, int current) {
		
		visited[current] = 4;
		for (int neighbour : graph.get(current)) {
			if (visited[neighbour] == 0) {
				dfs(graph, neighbour);
			}
			else if (visited[neighbour] == 4) {
				visited[current] = 3;
				index.get(1).add(current);
				return;
			}
			else if (visited[neighbour] == 1) {
				visited[neighbour] = 5;
				index.get(0).add(neighbour);
			}
		}
		visited[current] = 1;
		
	}
	
	public static void Solve(int n, int m, ArrayList<ArrayList<Integer>> graph) {
		
		visited = new int[n];
		index = new ArrayList<ArrayList<Integer>>(2);
		for (int i=0; i<2; i++) {
			index.add(new ArrayList<Integer>());
			
		}
		dfs(graph, 0);
		for (int i=0; i<2; i++) {
			int fillValue = 2;
			if (i == 1) {
				fillValue = -1;
			}
			for (int val : index.get(i)) {
				dfs2(graph, val, fillValue);
			}
		}
		for (int val : visited) {
			System.out.print(val + " ");
		}
		System.out.println();
		
	}

	public static void main(String[] args) {

		Scanner in = new Scanner(System.in);
		int t = in.nextInt();
		for (int i=0; i<t; i++) {
			int n = in.nextInt();
			int m = in.nextInt();
			ArrayList<ArrayList<Integer>> graph = new ArrayList<ArrayList<Integer>>(n);
			for (int j=0; j<n; j++) {
				graph.add(new ArrayList<Integer>());
			}
			for (int j=0; j<m; j++) {
				int node1 = in.nextInt()-1;
				int node2 = in.nextInt()-1;
				graph.get(node1).add(node2);
			}
			Solve(n, m, graph);
		}
		in.close();
		
	}

}