Possible dynamic programming and combinatorics

Can anyone please help for the approach of the question. It was asked in a previous competition.

Given a nm unshaded matrix, we need to find the no. Of ways to shade matrix such that every nn submatrix will have exactly k no. Of shaded cells.

m will always be greater than equal to n.

Here 1 <= k <= n*n
1 <= n <= 100
1 <= m <= 10^18

Input case
n
m
k
Output

4
5
1
28


1
3
1
1


5
37
1
1015625