Time Limit: 1000 MS    Memory Limit: 65536 K 

Description

After solving soj3591, 456 wants to know the maximum value of the sum of a continuous subsequence of a given number sequence where the length of the subsequence is at least k and how many subsequences' sum is the maximum value.

Input

The first line of the input is an integer T stdands the number of test cases. Then T test case follows. The first line of a test case is n and k. n is the length of the given sequence. The second contains n integers seperated by space. constraints: 1 <= k <= n <= 10^5 The absolute of the integers of the given sequence won't be greater than 10000.

Output

For each test case, output the maximum value and the count sepearted by a space in a single line.

Sample Input

2 3 2 1 2 3 3 2 1 2 -4

Sample Output

6 1 3 1

Author

456