1083: So Easy!

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题目描述

A sequence Sn is defined as:

Where a, b, n, m are positive integers.┌x┐is the ceil of x. For example, ┌3.14┐=4. You are to calculate Sn.
You, a top coder, say: So easy!

输入

There are several test cases, each test case in one line contains four positive integers: a, b, n, m. Where 0< a, m < 215, (a-1)2< b < a2, 0 < b, n < 231.The input will finish with the end of file.

输出

For each the case, output an integer Sn.

样例输入

2 3 1 2013
2 3 2 2013
2 2 1 2013


样例输出

4
14
4


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