## Editorial for DMOPC '21 Contest 3 P1 - Sums & Differences

**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:

#### Subtask 1

We only get two queries. How can we determine both of the numbers? We have two queries, but let's just use . Let's query it twice. We will show a simulation of the array based on hidden variables and :

The first query returns . The second returns . We can use the output of the second query to determine , and the output of the first to determine from that.

#### Subtask 2

There exists a solution here that makes queries and solves a system of equations (after all, it's just equations with variables). However, we omit it, since it is long. We instead proceed to the last subtask, which contains an easier solution.

#### Full Solution

The full solution simply applies the subtask solution to the first two indices, and then after that queries for . Since we already know one variable and we get the output of the query, then , where is the current value in position , and is the output of the query (since the output is ). We then need to set to .

We end with some advice: if a problem is challenging, look at the subtasks. The first subtask should be a good hint. Even on problems without subtasks, making your own subtasks is very often helpful for approaching the final solution.

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