ACM 2005 - Hamming Problem

Problem T. Hamming Problem ≡

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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 H_i(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 - H_i(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`