B. Equalize by Dividetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor 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.ExampleInput
10110031 1 122 125 534 3 243 3 4 422 10055 3 6 7 863 3 80 3 8 3419 40 19 55Output
0
0
-1
0
2
1 3
2 1
4
3 1
4 2
1 3
2 4
6
2 1
2 1
2 1
2 1
2 1
2 1
8
5 2
4 2
3 2
1 3
1 3
2 1
4 1
5 1
4
5 1
3 1
3 1
3 1
9
4 2
2 1
1 2
1 2
3 2
3 2
1 4
2 4
3 4
NoteIn the first and second, fourth test cases all numbers are equal, so it is possible to do nothing.In the third test case, it is impossible to make all numbers equal.In the fifth test case: [\color{red}{4}, 3, \color{blue}{2}] \to [\color{blue}{2}, \color{red}{3}, 2] \to [2, 2, 2].In the sixth test case: [\color{blue}{3}, 3, \color{red}{4}, 4] \to [3, \color{blue}{3}, 2, \color{red}{4}] \to [\color{red}{3}, 3, \color{blue}{2}, 2] \to [2, \color{red}{3}, 2, \color{blue}{2}] \to [2, 2, 2, 2].Here the red numbers are i indices (that will be assigned), blue numbers are j indices.
10110031 1 122 125 534 3 243 3 4 422 10055 3 6 7 863 3 80 3 8 3419 40 19 55
0 0 -1 0 2 1 3 2 1 4 3 1 4 2 1 3 2 4 6 2 1 2 1 2 1 2 1 2 1 2 1 8 5 2 4 2 3 2 1 3 1 3 2 1 4 1 5 1 4 5 1 3 1 3 1 3 1 9 4 2 2 1 1 2 1 2 3 2 3 2 1 4 2 4 3 4 
['brute force', 'constructive algorithms', 'greedy', 'math', '*1200']