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.