Migrated from Lutece 2353 Cooking

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Description

Potter needs to cook $n$ pieces of beef. Cooking a piece of beef needs $m$ steps and each step takes $t$ minutes. It's not necessary to cook a piece of beef continueously, which means after finishing one step, he can set the beef aside and cook another one. Potter is a skilled cook that he can deal with at most $k$ different pieces of beef at the same time.

Potter want to finish it as soon as possible. Please help him calculate how long will it take to finish cooking ?

Input

$n,m,k,t$

Output

An integer $T$, indicating that Potter has to spend at least $T$ minutes on cooking.

Samples

3 2 2 3

9

Constraints

$1≤n,m,k,t≤100$

Note

n=3 m=2 k=2 t=3

At the beginning : (0,0,0)

3min to deal with the first and the second : (1,1,0)

3min to deal with the first and the third : (2,1,1)

3min to deal with the second and the third : (2,2,2)

It takes 9 min totally.

Resources

电子科技大学第十届ACM趣味程序设计竞赛