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
sys.stderr = sys.stdout

from collections import deque


def solve(n, m, E):
    D = [[] for _ in range(n)]
    for u, v in E:
        D[u].append(v)

    P = [None] * n
    K = [0] * n
    V = [0] * n
    V[0] = 1
    A = {0}
    i = 0
    while i is not None:
        k = K[i]
        K[i] += 1
        if k < len(D[i]):
            j = D[i][k]
            if V[j] == 0:
                P[j] = i
                V[j] = 1
                A.add(j)
                i = j
            elif j in A:
                V[j] = -1
            elif V[j] == 1:
                V[j] = 2
        else:
            A.remove(i)
            i = P[i]

    Q = deque(i for i in range(n) if V[i] == -1)
    while Q:
        i = Q.pop()
        for j in D[i]:
            if V[j] != -1:
                V[j] = -1
                Q.append(j)
    Q = deque(i for i in range(n) if V[i] == 2)
    while Q:
        i = Q.pop()
        for j in D[i]:
            if V[j] == 1:
                V[j] = 2
                Q.append(j)
    return V


def reade():
    u, v = readinti()
    return u-1, v-1


def case():
    input()
    n, m = readinti()
    E = [reade() for _ in range(m)]
    return lstr(solve(n, m, E))


def main():
    t = readint()
    print('\n'.join(case() for _ in range(t)))

##########

def readint():
    return int(input())


def readinti():
   return map(int, input().split())


def readintt():
   return tuple(readinti())


def readintl():
   return list(readinti())


def readinttl(k):
    return [readintt() for _ in range(k)]


def readintll(k):
    return [readintl() for _ in range(k)]

def lstr(l):
    return ' '.join(map(str, l))

def llstr(ll):
    return '\n'.join(map(lstr, ll))


def log(*args, **kwargs):
    print(*args, **kwargs, file=sys.__stderr__)


if __name__ == '__main__':
    main()