F. Product transformationtime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputConsider 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 , 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.InputThe first and only line of input contains four integers N, M, a, Q (7 ≤ Q ≤ 109 + 123, 2 ≤ a ≤ 106 + 123, ,  is prime), where  is the multiplicative order of the integer a modulo Q, see notes for definition.OutputYou should output the array A from left to right.ExampleInput2 2 2 7Output1 2 NoteThe multiplicative order of a number a modulo Q , is the smallest natural number x such that ax mod Q = 1. For example, .
Input2 2 2 7
Output1 2 
['combinatorics', 'math', 'number theory', '*2200']