Victor and Machine

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 131072/65536 K (Java/Others)

Description

Victor has a machine. When the machine starts up, it will pop out a ball immediately. After that, the machine will pop out a ball every $w$ seconds. However, the machine has some flaws, every time after $x$ seconds of process the machine has to turn off for $y$ seconds for maintenance work. At the second the machine will be shut down, it may pop out a ball. And while it's off, the machine will pop out no ball before the machine restart.

Now, at the $0$ second, the machine opens for the first time. Victor wants to know when the $n$-th ball will be popped out. Could you tell him?

Input

The input contains several test cases, at most $100$ cases.

Each line has four integers $x$, $y$, $w$ and $n$. Their meanings are shown above。

$1\leq x,y,w,n\leq 100$.

Output

For each test case, you should output a line contains a number indicates the time when the $n$-th ball will be popped out.

Sample Input

2 3 3 3 98 76 54 32 10 9 8 100

Sample Output

10 2664 939

Hint

hujie

Source

BestCoder Round #52 (div.2)

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