B"This is the hard version of the problem. The only difference between the easy version and the hard version is the constraints on n . You can only make hacks if both versions are solved. A permutation of 1, 2, ldots, n is a sequence of n integers, where each integer from 1 to n appears exactly once. For example, [2,3,1,4] is a permutation of 1, 2, 3, 4 , but [1,4,2,2] isn't because 2 appears twice in it. Recall that the number of inversions in a permutation a_1, a_2, ldots, a_n is the number of pairs of indices (i, j) such that i < j and a_i > a_j . Let p and q be two permutations of 1, 2, ldots, n . Find the number of permutation pairs (p,q) that satisfy the following conditions: Print the number of such pairs modulo mod . Note that mod may not be a prime. The only line contains two integers n and mod ( 1 <= n <= 500 , 1 <= mod <= 10^9 ). Print one integer, which is the answer modulo mod . The following are all valid pairs (p,q) when n=4 . "...