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 ≤ 10⁹ + 123, 2 ≤ a ≤ 10⁶ + 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.