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:

def naiveSolve():
    

    
    return
    
from types import GeneratorType
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
    return wrappedfunc

def main():
    
    t=int(input())
    allans=[]
    for _ in range(t):
        input()
        n,m=readIntArr()
        adj=[[] for __ in range(n+1)]
        for __ in range(m):
            u,v=readIntArr()
            adj[u].append(v)
        
        visitCnts=[0]*(n+1)
        revisitedNodeCyc=set()
        revisitedNodeNonCyc=set()
        
        path=set()
        @bootstrap
        def dfs1(node):
            for nex in adj[node]:
                if visitCnts[nex]==1:
                    if nex in path:
                        revisitedNodeCyc.add(nex)
                    else:
                        revisitedNodeNonCyc.add(nex)
                else:
                    visitCnts[nex]+=1
                    path.add(nex)
                    yield dfs1(nex)
                    path.remove(nex)
            yield None
        path.add(1)
        visitCnts[1]=1
        dfs1(1)
        @bootstrap
        def dfsCyc(node):
            for nex in adj[node]:
                if visitCnts[nex]==1:
                    visitCnts[nex]=-1
                    yield dfsCyc(nex)
            yield None
        for cycNode in revisitedNodeCyc:
            if visitCnts[cycNode]==1:
                visitCnts[cycNode]=-1
                dfsCyc(cycNode)
        @bootstrap
        def dfsNonCyc(node):
            for nex in adj[node]:
                if visitCnts[nex]==1:
                    visitCnts[nex]=2
                    yield dfsNonCyc(nex)
            yield None
        for nonCycNode in revisitedNodeNonCyc:
            if visitCnts[nonCycNode]==1:
                visitCnts[nonCycNode]=2
                dfsNonCyc(nonCycNode)
        visitCnts.pop(0)
        allans.append(visitCnts)
        
    multiLineArrayOfArraysPrint(allans)
    
    return


import sys
input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
# input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.

def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
# def readFloatArr():
#     return [float(x) for x in input().split()]
 
def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])
    dv=defaultValFactory;da=dimensionArr
    if len(da)==1:return [dv() for _ in range(da[0])]
    else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
 
def queryInteractive(x):
    print('{}'.format(x))
    sys.stdout.flush()
    return int(input())
 
def answerInteractive(ans):
    print('! {}'.format(ans))
    sys.stdout.flush()
 
inf=float('inf')
# MOD=10**9+7
MOD=998244353

from math import gcd,floor,ceil
# from math import floor,ceil # for Python2
 
for _abc in range(1):
    main()