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.

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

inputFormat

outputFormat

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.

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

样例

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

1 0 1 2 -1 -1 
1
-1 -1 -1
1 0 0 0 0
1 1 2 1

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