Description

小明是一个喜欢收藏纪念币的人，但是他只喜欢那一种特定的纪念币，并且只有”N“枚。他的生日即将到来，所以他的”M

“个朋友决定一起送给他纪念币。但是纪念币比较昂贵，他的朋友决定送给小明最少个数纪念币。现在我们知道小明已经

拥有”K“个纪念币。

对于他朋友赠送硬币有以下要求：

一.他所有朋友赠送的硬币必须完全不同。

二.他从他朋友那里至少得到”L“个纪念币（得到的硬币所有硬币中不同有自己已经拥有的硬币个数为”L“）

Format

Input

The only line of input contains 4 integers N M K L(1≤K≤N≤1018, 1≤M,L≤1018)

(输入为多组输入！！！）

Output

Print one number — minimal number of coins one friend can gift to satisfy all the conditions. If it is impossible to satisfy all three conditions print "-1" (without quotes).

Samples

20 15 2 3
10 11 2 4

1
-1

Hint

In
the first test, one coin from each friend is enough, as he will be
presented with 15 different coins and 13 of them will definitely be
new.

In
the second test, Ivan has 11 friends, but there are only 10 different
coins. So all friends can't present him different coins.