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Smallest sequence with given Primes


Problem Setter: RAMBO_tejasv Problem Tester: aayushkapadia

Problem Description

GIven three prime numbers A, B and C and an integer D.

You need to find the first(smallest) D integers which only have A, B, C or a combination of them as their prime factors.



Input Format

First argument is an integer A.

Second argument is an integer B.

Third argument is an integer C.

Fourth argument is an integer D.



Output Format

Return an array of size D denoting the first smallest D integers which only have A, B, C or a combination of them as their prime factors.

NOTE: You need to return the array sorted in ascending order.



Example Input

Input 1:

 A = 2
 B = 3
 C = 5
 D = 5



Example Output

Output 1:

 [2, 3, 4, 5, 6]



Example Explanation

Explanation 1:

 4 = A * A i.e ( 2 * 2 ) 
 6 = A * B i.e ( 2 * 3 )



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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