A14445. AquaMoon and Two Arrays

AquaMoon and Cirno are playing an interesting game with arrays. Cirno has prepared two arrays $a$ and $b$ , both consist of $n$ non-negative integers. AquaMoon can perform the following operation an arbitrary number of times (possibly zero):

- She chooses two indices $i$ and $j$ ( $1 \le i, j \le n$ ), then decreases the $i$ -th element of array $a$ by $1$ , and increases the $j$ -th element of array $a$ by $1$ . The resulting values at $i$ -th and $j$ -th index of array $a$ are $a_i - 1$ and $a_j + 1$ , respectively. Each element of array $a$ must be non-negative after each operation. If $i = j$ this operation doesn't change the array $a$ .

AquaMoon wants to make some operations to make arrays $a$ and $b$ equal. Two arrays $a$ and $b$ are considered equal if and only if $a_i = b_i$ for all $1 \leq i \leq n$ .

Help AquaMoon to find a sequence of operations that will solve her problem or find, that it is impossible to make arrays $a$ and $b$ equal.

Please note, that you don't have to minimize the number of operations.

The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases.

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

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \leq a_i \leq 100$ ). The sum of all $a_i$ does not exceed $100$ .

The third line of each test case contains $n$ integers $b_1, b_2, \dots, b_n$ ( $0 \leq b_i \leq 100$ ). The sum of all $b_i$ does not exceed $100$ .

For each test case print "-1" on the only line if it is impossible to make two arrays equal with some sequence of operations.

Otherwise, print an integer $m$ ( $0 \leq m \leq 100$ ) in the first line — the number of operations. Then print $m$ lines, each line consists of two integers $i$ and $j$ — the indices you choose for the operation.

It can be proven that if it is possible to make two arrays equal with some sequence of operations, there exists a sequence with $m \leq 100$ .

If there are multiple possible solutions, you can print any.

In the first example, we do the following operations:

- $i = 2$ , $j = 1$ : $[1, 2, 3, 4] \rightarrow [2, 1, 3, 4]$ ;
- $i = 3$ , $j = 1$ : $[2, 1, 3, 4] \rightarrow [3, 1, 2, 4]$ ;

In the second example, it's impossible to make two arrays equal.