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Trulicina gives you integers $$$n$$$, $$$m$$$, and $$$k$$$. It is guaranteed that $$$k\geq 2$$$ and $$$n\cdot m\equiv 0 \pmod{k}$$$.

Output a $$$n$$$ by $$$m$$$ grid of integers such that each of the following criteria hold:

Each integer in the grid is between $$$1$$$ and $$$k$$$, inclusive.
Each integer from $$$1$$$ to $$$k$$$ appears an equal number of times.
No two cells that share an edge have the same integer.

It can be shown that such a grid always exists. If there are multiple solutions, output any.

Input

The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

The first line of each test case contains three integers $$$n$$$, $$$m$$$, and $$$k$$$ ($$$2 \leq n\cdot m\leq 2\cdot 10^5, 2\leq k\leq n\cdot m, n\cdot m\equiv 0 \pmod{k})$$$.

It is guaranteed that the sum of $$$n\cdot m$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Trulimero Trulicina

Examples