# UVa 516

## 516 - Prime Land[edit]

## Summary[edit]

For this problem you have to know what the Prime Base Representation of a number is.

Use the Prime Sieve of Eratosthenes to create an array of all prime numbers less or equal than 32767, and then use the array to factor numbers.

## Explanation[edit]

For the Prime Base Representation of a number you have to print the prime factors of the number and the frequency they appear in it's factorization (in decreasing order of prime factors). Something like this:

Where p is a decreasing sequence of primes and e is the corresponding sequence of powers of p. Each e must be greater than 0, so primes which are not factors are omitted from the prime base representation.

First you have to read a Prime Base Representation of a number and calculate just as you would expect by multiplying

Then you have to output the Prime Base Representation of .

For example, for the input5 1 2 1

Then

and

Therefore, the output is

3 2.

## Input[edit]

17 1 5 1 2 1 509 1 59 1 3 1 151 1 31 1 7 1 131 1 5 3 2 1 0

## Output[edit]

2 4 3 2 13 1 11 1 7 1 5 1 3 1 2 1 2 1 127 1 43 1 3 1 2 1 32749 1