So Easy!

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

Memory Limit: 32768/32768 K (Java/Others)

Description

  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!

Input

  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.

Output

  For each the case, output an integer Sn.

Sample Input

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

Sample Output

4 14 4

Hint

zhoujiaqi2010

Source

2013 ACM-ICPC长沙赛区全国邀请赛——题目重现

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