Level the Grid in Steps

Medium

You get a rectangular integer grid grid and a step step. One move adds step to any single cell or subtracts it from that cell. Return the fewest moves after which all cells hold the same value, or -1 if that is impossible.

Example 1

grid=[[3, 9], [6, 12]], step=3 → 4

Level everything to 6: raise 3 by one step, lower 9 by one step and 12 by two. That is 4 moves.

Example 2

grid=[[5, 7, 8]], step=2 → -1

5 and 7 are odd while 8 is even, so steps of 2 can never make them equal.

Example 3

grid=[[4], [4]], step=7 → 0

The cells are already equal.

Constraints

1 ≤ rows, columns
number of cells ≤ 10⁵
1 ≤ step ≤ 10⁴
1 ≤ grid[i][j] ≤ 10⁴

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Topics

Array Math Matrix Sorting

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Input

grid=[[3, 9], [6, 12]], step=3

Expected

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