A15857 | Equalize by Divide

You are given an array $a_1, a_2, \ldots, a_n$ of positive integers.

You can make this operation multiple (possibly zero) times:

- Choose two indices $i$ , $j$ ( $1 \leq i, j \leq n$ , $i \neq j$ ).
- Assign $a_i := \lceil \frac{a_i}{a_j} \rceil$ . Here $\lceil x \rceil$ denotes $x$ rounded up to the smallest integer $\geq x$ .

Is it possible to make all array elements equal by some sequence of operations (possibly empty)? If yes, print any way to do it in at most $30n$ operations.

It can be proven, that under the problem constraints, if some way exists to make all elements equal, there exists a way with at most $30n$ operations.

The first line contains a single integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases. Descriptions of test cases follow.

The first line of each test case description contains a single integer $n$ ( $1 \leq n \leq 100$ ).

The second line of each test case description contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10^9$ ).

It is guaranteed, that the sum of $n$ for all test cases does not exceed $1000$ .

For each test case print a single integer $q$ ( $-1 \leq q \leq 30n$ ). If $q=-1$ , there is no solution, otherwise $q$ is equal to the number of operations.

If $q \geq 0$ , on the next $q$ lines print two integers $i$ , $j$ ( $1 \leq i, j \leq n$ , $i \neq j$ ) — descriptions of operations.

If there are multiple solutions, you can print any.