[Probability DP] [Polynomial modulus] Noi2017.day1 T3 Swimming Pool

F (i,j) represents the height of I, the length of the local area of J, I this row there is a barrier, the former i-1 row does not have the barrier, can select the region <=k probability

So fi,j=∑k<jfi,k∗pi−1∗q∗gi,j−k−1+∑k<jgi,k∗gi,j−k−1∗pi−1∗q f I, J =∑k < J F I, k∗p i−1∗q∗g i, j−k− 1 +∑k < J G I, k∗g I, J−k−1∗p i−1∗q f_{i,j}=\sum_{k,
where p is the probability of a lattice safe, q, for a lattice dangerous probability.
Gi,j g I, J G_{i,j} represents the I row, there is no obstacle in the area of length J, the probability of the selected area <=k
So Gi,j=∑s>ifs,k g I, J =∑s > I f S, K g_{i,j}=\sum_{s>i}f_{s,k}

It's going to take a little bit of diversion.
Can be transferred by segment, set H (i) H (i) H (i) as the answer of length I
So H (i) =∑kj=1h (i−j) ∗g (1