## Editorial for DMOPC '21 Contest 5 P2 - Permutations & Primes

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**only**when stuck, and**not to copy-paste code from it**. Please be respectful to the problem author and editorialist.**Submitting an official solution before solving the problem yourself is a bannable offence.**Author:

The problem is essentially asking us to find a permutation of such that the prefix sums are not prime.

Starting with smaller cases of , we have the following outputs:

→ `1`

( is not composite or prime)

→ `-1`

→ `1 3 2`

For cases where , we can use the fact that the sum of the first natural numbers is , which is composite if . Proof is left as an exercise to the reader. From this, we note that if has a permutation for , then also has a valid permutation, where is just added to the end. This is because the prefix sum at will be .

**Time Complexity**:

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