A1316. [COCI-2015_2016-contest5]#4 PODNIZOVI

You are given an array of integers of length N. Let s1, s2, ..., sq be the lexicographically sorted array of all its non-empty subsequences. A subsequence of the array is an array obtained by removing zero or more elements from the initial array. Notice that some subsequences can be equal and that it holds q = 2N −
1.
An array A is lexicographically smaller than array B if Ai < Bi where i is the first position at which the arrays differ, or if A is a strict prefix of array B.
Let us define the hash of an array that consists of values v1, v2, ..., vp as:
h(s) = (v1 · Bp−1 + v2 · Bp−2 + ... + vp−1 · B + vp) mod M where B, M are given integers.
Calculate h(s1), h(s2), ..., h(sK) for a given K.

The first line contains integers N, K, B, M (1 6 N 6 100 000, 1 6 K 6 100 000, 1 6 B, M 6 1 000 000).
The second line contains integers a1, a2, a3, ..., aN (1 6 ai 6 100 000).
In all test cases, it will hold K 6 2 N −
1.

Output K lines, the j th line containing h(sj ).

In test cases worth 60% of total points, it will additionally hold 1 6 a1, a2, ..., aN 6 30.

Clarification of the first example: It holds: s1 = [1], s2 = [1, 2], s3 = [2]. h(s1) = 1 mod 5 = 1, h(s2) =
(1 + 2) mod 5 = 3, h(s3) = 2 mod 5 = 2.
Clarification of the second example: It holds: s1 = [1], s2 = [1], s3 = [1, 1], s4 = [1, 3]. h(s1) = 1
mod 3 = 1, h(s2) = 1 mod 3 = 1, h(s3) = (1 · 2 + 1) mod 3 = 0, h(s4) = (1 · 2 + 3) mod 3 = 2.