1547_G. How Many Paths?
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 
```python
import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10**7)

def scc_dfs1(s, links, status, postorder):
    stack = [s]
    status[s] = 0
    while stack:
        v = stack[-1]
        limit = len(links[v])
        while status[v] < limit:
            u = links[v][status[v]]
            status[v] += 1
            if status[u] != -1:
                continue
            stack.append(u)
            status[u] = 0
            break
        else:
            stack.pop()
            postorder.append(v)
    return


def scc_dfs2(s, rev_links, status):
    stack = [s]
    status[s] = -1
    scc = [s]
    while stack:
        v = stack.pop()
        for u in rev_links[v]:
            if status[u] != -1:
                stack.append(u)
                status[u] = -1
                scc.append(u)
    return scc


def strongly_connected_components(n, links, rev_links):
    status = [-1] * n
    postorder = []

    for v in range(n):
        if status[v] != -1:
            continue
        scc_dfs1(v, links, status, postorder)

    postorder.reverse()
    sccs = []

    for v in postorder:
        if status[v] == -1:
            continue
        sccs.append(scc_dfs2(v, rev_links, status))

    return sccs


def main():
    t = int(input()); INF = pow(10,18)
    for _ in range(t):
        dummy = input()
        n,m = map(int,input().split())
        G = [[] for _ in range(n)]
        RG = [[] for _ in range(n)]
        self_v = set([])
        for _ in range(m):
            a,b = map(int,input().split())
            a -= 1 ;b -= 1
            G[a].append(b)
            RG[b].append(a)
            if a == b:
                self_v.add(a)
        
        TT = strongly_connected_components(n, G, RG)
        #print(Group)
        #print(TT)
        ans = [0]*n
        ans[0] = 1
        for cluster in TT:
            if len(cluster) > 1:
                Flag = True
                for p in cluster:
                    if not Flag: break
                    for pre in RG[p]:
                        if ans[pre] == -1:
                            Flag = False
                            break
                        ans[p] += ans[pre]
                        if ans[p] > 0:
                            Flag = False
                            break
                if not Flag:
                    for p in cluster:
                        ans[p] = -1
                else:
                    for p in cluster:
                        ans[p] = 0
            else:
                p = cluster[0]
                if p in self_v:
                    Flag = True
                    for pre in RG[p]:
                        if ans[pre] == -1:
                            Flag = False
                            break
                        ans[p] += ans[pre]
                        if ans[p] > 0:
                            Flag = False
                            break
                    if not Flag:
                        ans[p] = -1
                else:
                    for pre in RG[p]:
                        if ans[pre] == -1:
                            ans[p] = -1
                            break
                        else:
                            ans[p] += ans[pre]
                            ans[p] = min(ans[p],2)
        print(*ans)




if __name__ == '__main__':
    main()
```