codeforces#P1546A. AquaMoon and Two Arrays
AquaMoon and Two Arrays
Description
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.
Input
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 $100$.
Output
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.
Samples
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
2
2 1
3 1
-1
0
6
1 4
1 4
1 5
1 5
2 5
2 5
Note
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.