Description

Lulichuan is the captain of SDNU ACM/ICPC TEAM, he have many team members, Their ability has a sequence from $1$ to $N$, now , lulichuan want to labeled them from $1$ to $N$ in this way

$a.$ Two member have different label

$b.$ The labeling satisfies several constrains like "The member labeled with $x$ is lower than the one labeled with $y$”.

Format

Input

The first line is $T$, $T$ is TestCase$(0 < T <= 1000)$

The first line of each testcase is two number $N, M(0 < 500 < n, 0 < M < 100000)$

The next $M$ line each contain two integers $x$ and $y$ indicating the member labeled with $x$ must be lower than the one labeled with $y$. $(1 ≤ x, y ≤ N)$

Output

For each test case output on a single line the member' ability from label $1$ to label $N$. If several solutions exist, you should output the one with the lowest ability for label $1$, then with the lowest ability for label $2$ and so on... If no solution exists, output $-1$ instead.

Samples

5
4 0

4 1
1 1

4 2
1 2
2 1

4 1
2 1

4 1
3 2

1 2 3 4
-1
-1
2 1 3 4
1 3 2 4