Subtask 1

We only get two queries. How can we determine both of the numbers? We have two queries, but let's just use $(1,2)$. Let's query it twice. We will show a simulation of the array based on hidden variables $a$ and $b$:

$${\displaystyle \{a,b\}}$$ $${\displaystyle \{a+b,a-b\}}$$ $${\displaystyle \{2a,2b\}}$$

The first query returns $a-b$. The second returns $2b$. We can use the output of the second query to determine $b$, and the output of the first to determine $a$ from that.

Subtask 2

There exists a solution here that makes $3$ queries and solves a system of equations (after all, it's just $3$ equations with $3$ 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 $1$ solution to the first two indices, and then after that queries $(1,i)$ for $i\ge 3$. Since we already know one variable and we get the output of the query, then $a_i=x-k$, where $x$ is the current value in position $1$, and $k$ is the output of the query (since the output is $x-a_i$). We then need to set $x$ to $x+a_i$.

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.