Allowance (3) X30229

You have saved $n$ euros. Additionally, every Monday of the forthcoming weeks you will be given a weekly allowance. On odd weeks, you get $a_o$ euros, while on even weeks you will receive $a_e$ euros. On the $i$-th week, your amount of expenses sums up to $d_i$ euros. The first week is the week $i=1$ and, therefore, it is an odd week.

Write a program that computes the balance at the end of each week.

Input

The input consists of three natural numbers, $a_o \geq 0$, $a_e \geq 0$ and $n \geq 0$. Representing the allowance on odd weeks, the allowance on even weeks and the initial savings, respectively.

Following, there is a non-empty sequence of natural numbers where each element $d_i\geq 0$. Each element $d_i$ represents the expenses of the $i$-th week.

Output

The output is a sequence of integers. Each element of this sequence $b_i$ indicates the balance at the end of the $i$-th week, once the corresponding expenses are payed.

Follow the format specified in the examples. Your code should follow the rules of style and contain the comments that you deem appropriate.