852F · Product transformation

Problem: Consider an array A with N elements, all being the same integer a.

Define the product transformation as a simultaneous update Ai = Ai·Ai + 1, that is multiplying each element to the element right to it for $i \in (1, 2,..., N-1)$, with the last number AN remaining the same. For example, if we start with an array A with a = 2 and N = 4, then after one product transformation A = [4, 4, 4, 2], and after two product transformations A = [16, 16, 8, 2].

Your simple task is to calculate the array A after M product transformations. Since the numbers can get quite big you should output them modulo Q.

Input Format: The first and only line of input contains four integers N, M, a, Q (7 ≤ Q ≤ 109 + 123, 2 ≤ a ≤ 106 + 123, $1 \leq M, N < \phi(a, Q) \leq 10^6 + 123$, $\phi(a,Q)$ is prime), where $\phi(a,Q)$ is the multiplicative order of the integer a modulo Q, see notes for definition.

Output Format: You should output the array A from left to right.

Note: The multiplicative order of a number a modulo Q $\phi(a,Q)$, is the smallest natural number x such that ax mod Q = 1. For example, $\phi(2,7)=3$.