For each three prime numbers p₁, p₂ and p₃, let’s 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

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

p₁, p₂ and p₃ are different prime numbers.

Output

 The output file must contain the single integer — H_i(p₁, p₂, p₃). All numbers in input and output are less than 10¹⁸.