Consider an array A with N elements, all being the same integer a . Define the product transformation as a simultaneous update A i = A i · A i + 1 , that is multiplying each element to the element right to it for , with the last number A N 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 . The first and only line of input contains four integers N , M , a , Q ( 7 ≤ Q ≤ 10 9 + 123 , 2 ≤ a ≤ 10 6 + 123 , , is prime), where is the multiplicative order of the integer a modulo Q , see notes for definition. You should output the array A from left to right. The multiplicative order of a number a modulo Q , is the smallest natural number x such that a x mod Q = 1 . For example, .