B"We call an array a of length n fancy if for each 1 < i <= n it holds that a_i = a_{i-1} + 1 . Let's call f(p) applied to a permutation ^ dagger of length n as the minimum number of subarrays it can be partitioned such that each one of them is fancy. For example f([1,2,3]) = 1 , while f([3,1,2]) = 2 and f([3,2,1]) = 3 . Given n and a permutation p of length n , we define a permutation p' of length n to be k -special if and only if: Your task is to count for each 1 <= k <= n the number of k -special permutations modulo m . ^ dagger A permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation ( 2 appears twice in the array) and [1,3,4] is also not a permutation ( n=3 but there is 4 in the array). ^ ddagger A permutation a of length n is lexicographically smaller than a permutation b of length n if and only if the following holds: in the first position where a and b differ, the permutation a has a smaller element than the corresponding element in b . The first line contains two integers n and m ( 1 <= n <= 2000 , 10 <= m <= 10^9 ) -- the length of the permutation and the required modulo. The second line contains n distinct integers p_1, p_2, ldots, p_n ( 1 <= p_i <= n ) -- the permutation p . Print n integers, where the k -th integer is the number of k -special permutations modulo m . In the first example, the permutations that are lexicographically smaller than [1,3,4,2] are: Thus our answer is [1,0,1,1] . In the second example, the permutations that are lexicographically smaller than [3,2,1] are: Thus our answer is [1,2,2] . "...