A11266. Product transformation

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, .