You are asked to build an array $$$a$$$, consisting of $$$n$$$ integers, each element should be from $$$1$$$ to $$$k$$$.

The array should be non-decreasing ($$$a_i \le a_{i+1}$$$ for all $$$i$$$ from $$$1$$$ to $$$n-1$$$).

You are also given additional constraints on it. Each constraint is of one of three following types:

$$$1~i~x$$$: $$$a_i$$$ should not be equal to $$$x$$$;
$$$2~i~j~x$$$: $$$a_i + a_j$$$ should be less than or equal to $$$x$$$;
$$$3~i~j~x$$$: $$$a_i + a_j$$$ should be greater than or equal to $$$x$$$.

Build any non-decreasing array that satisfies all constraints or report that no such array exists.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.

The first line of each testcase contains three integers $$$n, m$$$ and $$$k$$$ ($$$2 \le n \le 2 \cdot 10^4$$$; $$$0 \le m \le 2 \cdot 10^4$$$; $$$2 \le k \le 10$$$).

The $$$i$$$-th of the next $$$m$$$ lines contains a description of a constraint. Each constraint is of one of three following types:

$$$1~i~x$$$ ($$$1 \le i \le n$$$; $$$1 \le x \le k$$$): $$$a_i$$$ should not be equal to $$$x$$$;
$$$2~i~j~x$$$ ($$$1 \le i \lt j \le n$$$; $$$2 \le x \le 2 \cdot k$$$): $$$a_i + a_j$$$ should be less than or equal to $$$x$$$;
$$$3~i~j~x$$$ ($$$1 \le i \lt j \le n$$$; $$$2 \le x \le 2 \cdot k$$$): $$$a_i + a_j$$$ should be greater than or equal to $$$x$$$.

The sum of $$$n$$$ over all testcases doesn't exceed $$$2 \cdot 10^4$$$. The sum of $$$m$$$ over all testcases doesn't exceed $$$2 \cdot 10^4$$$.

Output

For each testcase, determine if there exists a non-decreasing array that satisfies all conditions. If there is no such array, then print -1. Otherwise, print any valid array — $$$n$$$ integers from $$$1$$$ to $$$k$$$.

Too Many Constraints

Examples