Problem T. Hamming Problem

Author:Far-Eastern Subregional   Time limit:3 sec
Input file:input.txt   Memory limit:8 Mb
Output file:output.txt  

Statement

For each three prime numbers p1, p2 and p3, letis 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 file format

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

Output file format

The output file must contain the single integer - Hi(p1, p2, p3).

Constraints

All numbers in input and output are less than 1018.

Sample tests

No. Input file (input.txt) Output file (output.txt)
1
7 13 19 100
26590291

0.063s 0.010s 13