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 CPP):

Solution:
#include <bits/stdc++.h>
#define forn(i,n) for(ll i=0; i<n; i++)
#define pb push_back
#define ll long long int
#define mp make_pair
#define sz(arr) (ll)arr.size()
#define MOD 998244353

using namespace std;

vector< vector<ll> > tree;
vector<ll> ans,used;
void dfs(ll nd){
	used[nd]=1;
	//cout<<nd<<" ";
	for(ll nxt: tree[nd]){
		if (ans[nxt]==0){
			ans[nxt]=ans[nd];
			dfs(nxt);
		}
		else{
			if (used[nxt]==0 and ans[nxt]==1){
				ans[nxt]=2;
				dfs(nxt);
			}
			if (used[nxt]==1 and ans[nxt]!=-1){
				ans[nxt]=-1;
				//dfs(nxt);
			}
		}

	}
	
	used[nd]=0;
}

void second_dfs(ll nd){
	for(ll nxt: tree[nd]){
		if (ans[nxt]!=-1){
			ans[nxt]=-1;
			second_dfs(nxt);
		}
	}
}

void solve(){
	ll n,m;
	cin>>n>>m;
	tree=vector< vector<ll> > (n);
	ll x,y;
	forn(i,m){
		cin>>x>>y;
		x--;y--;
		tree[x].pb(y);
	}
	
	ans=vector<ll>(n,0);
	used=vector<ll>(n);
	ans[0]=1;
	dfs(0);
	forn(i,n) if (ans[i]==-1) second_dfs(i);
	
	forn(i,n) cout<<ans[i]<<" ";
	cout<<"\n";
}

int main(){
	ll T;
	cin>>T;
	while (T--){
		solve();
	}
}