The Berland Army is preparing for a large military parade. It is already decided that the soldiers participating in it will be divided into k rows, and all rows will contain the same number of soldiers.

Of course, not every arrangement of soldiers into k rows is suitable. Heights of all soldiers in the same row should not differ by more than 1. The height of each soldier is an integer between 1 and n.

For each possible height, you know the number of soldiers having this height. To conduct a parade, you have to choose the soldiers participating in it, and then arrange all of the chosen soldiers into k rows so that both of the following conditions are met:

  * each row has the same number of soldiers, 
  * no row contains a pair of soldiers such that their heights differ by 2 or more. 



Calculate the maximum number of soldiers who can participate in the parade.

Input

The first line contains one integer t (1 ≤ t ≤ 10000) — the number of test cases. Then the test cases follow. 

Each test case begins with a line containing two integers n and k (1 ≤ n ≤ 30000, 1 ≤ k ≤ 10^{12}) — the number of different heights of soldiers and the number of rows of soldiers in the parade, respectively.

The second (and final) line of each test case contains n integers c_1, c_2, ..., c_n (0 ≤ c_i ≤ 10^{12}), where c_i is the number of soldiers having height i in the Berland Army.

It is guaranteed that the sum of n over all test cases does not exceed 30000.

Output

For each test case, print one integer — the maximum number of soldiers that can participate in the parade.

Example

Input


5
3 4
7 1 13
1 1
100
1 3
100
2 1
1000000000000 1000000000000
4 1
10 2 11 1


Output


16
100
99
2000000000000
13

Note

Explanations for the example test cases:

  1. the heights of soldiers in the rows can be: [3, 3, 3, 3], [1, 2, 1, 1], [1, 1, 1, 1], [3, 3, 3, 3] (each list represents a row); 
  2. all soldiers can march in the same row; 
  3. 33 soldiers with height 1 in each of 3 rows; 
  4. all soldiers can march in the same row; 
  5. all soldiers with height 2 and 3 can march in the same row.

Source: codeforces | Difficulty: MEDIUM_HARD
Tags: Sorting

Greedy algorithms


Solutions: