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:
import sys
from collections import deque

input = sys.stdin.readline

def kosaraju(n,G):
    # return ans[i] = group symbol for node i, W: condensed graph
    T = [[] for _ in range(n)]

    for i in range(n):
        for j in G[i]:
            T[j].append(i)

    L = []
    vis = [-1]*n
    ans = [-1]*n

    for u in range(n):
        if vis[u] != -1:
            continue

        stk = [u]
        while stk:
            w = stk[-1]
            if vis[w] == -1:
                vis[w] = 0
                for v in G[w]:
                    if vis[v] != -1: continue
                    stk.append(v)
            else:
                stk.pop()
                if vis[w] == 0:
                    vis[w] = 1
                    L.append(w)
   
    gp_symbol = -1
    while L:
        u = L.pop()
        if ans[u] == -1:
            gp_symbol += 1

            stk = [u]
            while stk:
                w = stk.pop()
                if ans[w] == -1:
                    ans[w] = gp_symbol
                    for v in T[w]:
                        if ans[v] == -1:
                            stk.append(v)

    W = [[] for _ in range(gp_symbol+1)]
    cyc = [False]*len(W)
    sz = [0]*len(W)

    for i in range(n):
        sz[ans[i]] += 1
        for j in G[i]:
            if ans[i] != ans[j]:
                W[ans[i]].append(ans[j])
            elif i == j:
                cyc[ans[i]] = True

    return ans, W, cyc, sz

def solve():
    _ = input()
    n,m = map(int,input().split())

    G = [[] for _ in range(n)]

    for _ in range(m):
        i,j = map(int,input().split())
        G[i-1].append(j-1)

    ref, W, cyc, sz = kosaraju(n,G)
    A = [0]*len(W)
    
    q = deque([(ref[0],0)])

    while q:
        node, prev = q.popleft()
        if A[node] in [2,-1] and prev != -1:            
            continue

        if prev == 0:
            if ref[0] == node:
                if sz[node] > 1 or cyc[node]:
                    A[node] = -1
                else:
                    A[node] = 1
        elif prev == 1:
            if A[node] == 0:
                A[node] = 1
            else:
                A[node] = 2
        elif prev == 2:
            A[node] = 2
        else:
            A[node] = -1

        if sz[node] > 1 or cyc[node]:
            A[node] = -1

        for node0 in W[node]:
            q.append((node0, A[node]))

    ans = [-99]*n

    for i in range(n):
        ans[i] = A[ref[i]]

    print(*ans)

for nt in range(int(input())):
    solve()