Your solution has complexity of O(N) per single tower, which results in O(m*N) per test-case which unfortunately is not fast enough. One could easily notice, however, that the dp states will be the same for the same K and L and are independent of N, so you can compute the states only for the largest tower (biggest N), thus resulting in O(N) per test-case.

I managed to get AC modifying your code to do just that, so feel free to ask any questions :)

hey.. can you please give me any hints on writing a recursive solution to this problem.. I would be so grateful if you do :D