# #P852F. Product transformation

ID: 3417 Type: RemoteJudge 3000ms 256MiB 尝试: 1 已通过: 1 难度: 8 上传者: 标签>combinatoricsmathnumber theory*2200

# Product transformation

## Description

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 , 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.

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.

## Input

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.

## Output

You should output the array A from left to right.

## Samples

``````2 2 2 7

``````
``````1 2
``````

## Note

The multiplicative order of a number a modulo Q , is the smallest natural number x such that ax mod Q = 1. For example, .