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 CPP):

Solution:
#include <iostream>
#include <cstring>
#include <cmath>
#include <cstdio>
using namespace std;
const int MAXVER = 4e5 + 5;

struct edge {
	int to, next;
	edge() {
		to = next = 0;
	}
	edge(int _to, int _next) {
		to = _to, next = _next;
	}
} edgeData[MAXVER];
int firstEdge[MAXVER];
void addEdge(int i, int from, int to) {
	edgeData[i] = edge(to, firstEdge[from]);
	firstEdge[from] = i;
}

int n, m, paths[MAXVER];
bool vis[MAXVER];
void init() {
	memset(firstEdge, 0, sizeof(firstEdge));

	memset(paths, 0, sizeof(paths));
	memset(vis, false, sizeof(vis));
}

void dfs(int pos, bool infinite) {
	vis[pos] = true;
	paths[pos] = infinite ? -1 : (paths[pos] == 0 ? 1 : 2);
	for(int i = firstEdge[pos]; i; i = edgeData[i].next) {
		int to = edgeData[i].to;
		if((infinite || vis[to]) && paths[to] != -1) {
			dfs(to, true);
		}
		else if(!vis[to] && paths[to] == 1) {
			dfs(to, infinite);
		}
		else if(paths[to] == 0) {
			dfs(to, infinite);
		}
	}
	vis[pos] = false;
}

int main() {
	int t;
	scanf("%d", &t);
	while(t--) {
		scanf("%d%d", &n, &m);
		init();
		for(int i = 1; i <= m; i++) {
			int from, to;
			scanf("%d%d", &from, &to);
			addEdge(i, from, to);
		}
		dfs(1, false);
		for(int i = 1; i <= n; i++) {
			printf("%d ", paths[i]);
		}
		printf("\n");
	}
}
/*
1
10 9
1 2
1 6
3 4
5 6
3 3
6 8
8 2
6 4
2 3
*/