CF1546A 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.