B'Ember and Storm play a game. First, Ember picks a labelled tree T of n vertices, such that the degree of every vertex is at most d. Then, Storm picks two distinct vertices u and v in this tree and writes down the labels of the vertices in the path from u to v in a sequence a1, xe2 x80 x89a2... ak. Finally, Ember picks any index i (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89i xe2 x80 x89< xe2 x80 x89k) in the array. Now he performs one of the following two operations exactly once: Ember wins if the array is monotonically increasing or decreasing after this. Otherwise Storm wins. The game can be described by the tuple (T, xe2 x80 x89u, xe2 x80 x89v, xe2 x80 x89i, xe2 x80 x89op) where op is xc2 xabflip xc2 xbb or xc2 xabnegate xc2 xbb depending on the action Ember chose in the last turn. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally, if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves. Report the answer modulo m. The input consists of a single line containing three integers n, d and m (2 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89200, xe2 x80 x891 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89d xe2 x80 x89< xe2 x80 x89n, xe2 x80 x891 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89m xe2 x80 x89 xe2 x89 xa4 xe2 x80 x892 xc2 xb7109). Print a single number -- the number of possible tuples if Ember and Storm play as described, modulo m. In the first sample case, there is only one possible tree. There are two possible paths, 1 to 2 and 2 to 1. For both paths, i can only be 1, and op can take both possibilities. Therefore, the answer is 4. In the second sample, there are no possible trees. In the third sample, there are three possible trees. '...