Product transformation

3000ms

262144K

Description:

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 $\text{[math]}$ , 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.

Input:

The first and only line of input contains four integers N, M, a, Q (7 ≤ Q ≤ 10⁹ + 123, 2 ≤ a ≤ 10⁶ + 123, $\text{[math]}$ , $\text{[math]}$ is prime), where $\text{[math]}$ is the multiplicative order of the integer a modulo Q, see notes for definition.

Output:

You should output the array A from left to right.

Sample Input:

2 2 2 7

Sample Output:

1 2

Note:

The multiplicative order of a number a modulo Q $\text{[math]}$ , is the smallest natural number x such that a^x mod Q = 1. For example, $\text{[math]}$ .

Informação

Provedor Codeforces

Código CF852F