Problem C: CF1416B Make Them Equal

# CF1416B Make Them Equal

## 题目描述

You are given an array $ a $ consisting of $ n $ positive integers numbered from $ 1 $ to $ n $ . You can perform the following operation no more than $ 3n $ times:

1. choose three integers $ i $ $ j $ and $ x $ ( $ 1 \le i j \le n $ ; $ 0 \le x \le 10^9 $ );
2. assign $ a_i := a_i - x \cdot i $ $ a_j := a_j + x \cdot i $ .

After each operation all elements of the array should be non-negative.

Can you find a sequence of no more than $ 3n $ operations after which all elements of the array are equal?

简述：每次选择 $i j x(1\leq i j \leq n 0\leq x \leq 10^9)$，令 $a_i$ 减去 $xi$，$a_j$ 加上 $xi$，要求 $a$ 永远非负，请输出一种操作次数不超过 $3n$ 的方案使得最终所有 $a_i$ 相等  

大家可以先在这里提交代码，如果想获取评测结果可以去 https://codeforces.com/problemset/problem/1416/B

## 输入格式

The first line contains one integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Then $ t $ test cases follow.

The first line of each test case contains one integer $ n $ ( $ 1 \le n \le 10^4 $ ) — the number of elements in the array. The second line contains $ n $ integers $ a_1 a_2 \dots a_n $ ( $ 1 \le a_i \le 10^5 $ ) — the elements of the array.

It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^4 $ .

## 输出格式

For each test case print the answer to it as follows:

- if there is no suitable sequence of operations print $ -1 $ ;
- otherwise print one integer $ k $ ( $ 0 \le k \le 3n $ ) — the number of operations in the sequence. Then print $ k $ lines the $ m $ -th of which should contain three integers $ i $ $ j $ and $ x $ ( $ 1 \le i j \le n $ ; $ 0 \le x \le 10^9 $ ) for the $ m $ -th operation.

If there are multiple suitable sequences of operations print any of them. Note that you don't have to minimize $ k $ .

## 输入输出样例 #1

### 输入 #1

```
3
4
2 16 4 18
6
1 2 3 4 5 6
5
11 19 1 1 3
```

### 输出 #1

```
2
4 1 2
2 3 3
-1
4
1 2 4
2 4 5
2 3 3
4 5 1
```