JOIN

 Problem Statement

Problem Statement for TheKingsFactorization

### Problem Statement

The King of Byteland likes integer factorization. Your task is to help him factor the number N. You will be given the long N and you should return a long[] containing all prime factors of N sorted in non-decreasing order. Note that some primes may occur multiple times in the prime factorization of N. For example, for N = 60 the only correct return value is {2, 2, 3, 5} because 2*2*3*5 = 60.

To make this task easier, the King has decided to give you a hint. He already knows the correct factorization and he will tell you every second number in the correct return value. More precisely, in addition to N you will be given a long[] primes. The number of elements in primes will be (M+1)/2, rounded down, where M is the number of elements in the correct return value. For each valid i, primes[i] will be equal to the element 2i of the correct return value. (All indices are 0-based.)

Given N and primes, return the long[] containing the factorization of N.

### Definition

 Class: TheKingsFactorization Method: getVector Parameters: long, long[] Returns: long[] Method signature: long[] getVector(long N, long[] primes) (be sure your method is public)

### Constraints

-N will be between 2 and 1,000,000,000,000,000,000 (10^18), inclusive.
-primes will contain the correct prime factors (as defined in the problem statement).

### Examples

0)

 `12` `{2, 3}`
`Returns: {2, 2, 3 }`
1)

 `7` `{7}`
`Returns: {7 }`
2)

 `1764` `{2, 3, 7}`
`Returns: {2, 2, 3, 3, 7, 7 }`
3)

 `49` `{7}`
`Returns: {7, 7 }`
4)

 `210` `{2, 5}`
`Returns: {2, 3, 5, 7 }`
5)

 `100000` `{2, 2, 2, 5, 5}`
`Returns: {2, 2, 2, 2, 2, 5, 5, 5, 5, 5 }`

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This problem was used for:
Single Round Match 643 Round 1 - Division I, Level One
Single Round Match 643 Round 1 - Division II, Level Two