AquaMoon and Two Arrays

题意翻译

现有两个各含有 $n$ 个非负整数的数组 $a, b$ ，您可以做以下若干次操作（可以是 $0$ 次）： - 选取两个数 $i, j$（$1 \leq i, j \leq n$），让 $a$ 数组的第 $i$ 个数减 $1$，第 $j$ 个数加 $1$ 。在每次操作后， $a$ 数组中的任何一个数必须仍为非负整数，如果 $i = j$，那么这个操作不会改变数组 $a$。 现求能否通过一些操作让数组 $a$ 变成 $b$（即 $\forall i \in [1, n], a_i = b_i$）。 请注意，您不需要让操作数量最小，但是你必须保证操作数量 $\le 100$。可以证明如果可以通过一些操作让数组 $a$ 变成 $b$，则存在一种操作序列的操作数量 $\le 100$。

题目描述

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.

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

4
4
1 2 3 4
3 1 2 4
2
1 3
2 1
1
0
0
5
4 3 2 1 0
0 1 2 3 4

输出样例 #1

2
2 1
3 1
-1
0
6
1 4
1 4
1 5
1 5
2 5
2 5

说明

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.