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 PYTHON3):

Solution:
from collections import deque
def cyc(n,path):
    visi,poi = [2]+[0]*(n-1),[0]*n;    inf = [];    multi = [];    st = [0]
    while len(st):
        x,y = st[-1],poi[st[-1]]
        if y == len(path[x]): visi[st.pop()] = 1
        else:
            z = path[x][y]
            if visi[z] == 2:   inf.append(z);   poi[x] += 1;    continue
            if visi[z] == 1:   multi.append(z);   poi[x] += 1;   continue
            st.append(z);    poi[x] += 1;  visi[z] = 2
    ans = [1]*n
    for i in range(n):
        if not visi[i]:   ans[i] = 0
    curr = deque(multi);    vv = [0]*n
    for i in multi: vv[i] = 1
    while len(curr):
        x = curr.popleft();   ans[x] = 2
        for y in path[x]:
            if not vv[y]:  vv[y] = 1;     curr.append(y)
    curr = deque(inf);    vv = [0]*n
    for i in inf: vv[i] = 1
    while len(curr):
        x = curr.popleft();    ans[x] = -1
        for y in path[x]:
            if not vv[y]: vv[y] = 1;   curr.append(y)
    return ans
for _ in range(int(input())):
    input();        n,m = map(int,input().split());        path = [[] for _ in range(n)]
    for _ in range(m):  aa,bb = map(int,input().split());       path[aa-1].append(bb-1)
    print(*cyc(n,path))