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Language:
Hamming Problem
 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 6683 Accepted: 3089

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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