This problem was asked in recent CodeNation Online Test

Given A,B,C — Count the number of valid arrays of size "A" — such that each number of the array is in the range [1,C] — and no subarray of length > B exists in the valid array such that all elements of that subarray are equal

1<=A<=10^9

1<=B<=50

1<=C<=10^5

A = 3

B = 1

C = 3

O/P — 12

[121],[123],[131],[132],[213],[212],[231],[232],[312],[313],[321],[323] are all valid arrays.

Idea = Valid Arrays = Total — Invalid arrays = Counting of Invalid Arrays is easier than valid arrays as far as I can conclude.