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Hamming Problem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2137    Accepted Submission(s): 921


Problem Description
For each three prime numbers p1, p2 and p3, let's define Hamming sequence Hi(p1, p2, p3), i=1, ... as containing in increasing order all the natural numbers whose only prime divisors are p1, p2 or p3.

For example, H(2, 3, 5) = 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, ...

So H5(2, 3, 5)=6.
 

Input
In the single line of input file there are space-separated integers p1 p2 p3 i.
 

Output
The output file must contain the single integer - Hi(p1, p2, p3). All numbers in input and output are less than 10^18.
 

Sample Input
7 13 19 100
 

Sample Output
26590291
 

Source
Northeastern Europe 2000 - Far-Eastern Subregion
 

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