The chef is preparing ~m~ dishes, and each dish uses ~k~ grams of ingredients. As a result, the chef has bought ~n~ ingredients, and the ingredients are numbered ~1, 2, \dots, n~. The ~i~-th ingredient weighs ~d_i~ grams. The sum of weights of all ~n~ ingredients is exactly ~m \times k~ grams. ~d_i~ and ~k~ are positive integers.

An ingredient may be used in multiple dishes. However, each dish may use at most 2 ingredients. Now you are asked to decide if there exists a valid way to prepare the ~m~ dishes. More formally, the final plan shall satisfy the following requirements:

1. Prepare ~m~ dishes in total.

2. Each dish uses at most 2 ingredients.

3. Each dish uses exactly ~k~ grams of ingredients.

4. For each ingredient used in a given dish, the amount used is a positive integer measured in grams.

5. All of the ~n~ ingredients will be completely utilized.

If there exists a feasible solution, you should output a detailed plan.

Input Specification

In this problem, each test case may have multiple instances. The first line is an integer ~T~ denoting the number of instances. For each instance, the first line contains three positive integers ~n,m,k~ denoting the number of ingredients, the number of dishes to prepare, and the amount of ingredients each dish uses. The second line contains ~n~ integers, and the ~i~-th integer denotes there are ~a_i~ grams of ingredient ~i~.

Output Specification

For each instance, if there is no feasible solution, output -1. Otherwise, you need to output ~m~ lines, and each line specifies the way to prepare a dish. Depending on the number of ingredients used in the dish, a line shall be in one of the following two formats:

• a line containing two integers ~i~ and ~x~ denoting the dish will use ~x~ grams of ingredient ~i~. Here, ~1 \le i \le n~ and ~x = k~.
• a line containing four integers ~i,x,j,y~ denoting the dish will use ~x~ grams of ingredient ~i~ and ~y~ grams of ingredient ~j~. Here, ~1 \le i,j \le n~, ~i \ne j~, ~x+y = k~, ~x, y > 0~.

Your answer will be checked by a special judge. Therefore, if there are multiple feasible solutions, you may print any solution. You should make sure the output is in the correct format, and two adjacent integers in a line are separated by a single space. Finally, your output shall not contain any extra characters.

Sample Input

4
1 1 10
10
4 3 100
80 30 90 100
5 3 1000
200 400 500 900 1000
6 4 100
25 30 50 80 95 120

Sample Output

1 10
1 80 2 20
2 10 3 90
4 100
-1
1 5 5 95
1 20 4 80
2 30 6 70
3 50 6 50

For all test cases:
~1 \le T \le 10~, ~1 \le n \le 500~, ~n-2 \le m \le 5000~, ~m \ge 1~,
~1 \le k \le 5000~, ~\sum\limits_{i=1}^n d_i = m \times k~.

Test case	~n~	~m~	~k~
1~3	~\le 4~	~\le 4~	~\le 50~
4~5	~\le 10~	~\le 10~	~\le 5000~
6~7	~\le 500~	~= n-1~
8~9		~n-1 \le m \le 5000~
10	~\le 25~	~\le 5000~
11~12			~\le 500~
13~14	~\le 50~
15~17	~\le 100~		~\le 5000~
18~20	~\le 500~