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 PYTHON):

Solution:
I=lambda: map(int, raw_input().split())
t = input()
for _ in xrange(t):
	raw_input()
	n,m = I()
	d = {}
	for _ in xrange(m):
		a,b = I()
		if a not in d:
			d[a] = []
		d[a].append(b)
	s = [(1, False, False)]
	rD = [0]*(n+1)
	colors = [0]*(n+1)
	while s:
		q, lp, ld = s.pop()
		# print q, lp, ld
		# print colors
		if q is None:
			colors[lp] = 2
			continue
		skip = False
		if colors[q] == 1:
			lp = True
		if lp:
			if rD[q] == -1:
				skip = True
			rD[q] = -1
		elif ld:
			if (rD[q] == 2 or rD[q] == -1):
				skip = True
			else:
				rD[q] = 2
		else:
			if rD[q]==0:
				rD[q] = 1
			elif rD[q]==1:
				rD[q] = 2
				ld = True
			else:
				skip = True
		if q in d and not skip:
			colors[q] = 1
			s.append((None, q, None))
			w = d[q]
			for x in w:
				s.append((x, lp, ld))
		else:
			colors[q] = 2
		
	rLst = []
	for i in xrange(1, n+1):
		rLst.append(str(rD[i]))
	print ' '.join(rLst)