CF2094F Trulimero Trulicina

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.

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 $ .

For each test case, output $ n $ lines, each containing $ m $ integers that satisfy the criteria. If there are multiple solutions, output any.