Phoebe enjoys playing music. She especially enjoys playing it for her friends.

Phoebe has made a new musical instrument. The instrument is very much like a piano. It has N keys arranged in a straight line, numbered from 1 to N. The i^th key has volume V_i. No two keys have the same volume and 1 ≤ V_i ≤ N. It takes |i-j| time to move from the i^th key to the j^th key on the instrument. Phoebe has a unique way of playing music. Immediately after playing key i, she can play only a key j such that:

• j is not closer than K positions from key i (i.e. j should not be in the range [ i-K+1, i+K-1 ]).

• V_j < V_i.

Each key may have 0 or more keys that can be played immediately after it.

Phoebe wants to find the summation of time required to go from each key i to the closest key that can be played after it. If there is no next playable key for a key i, then consider its time taken as 0.

Input:

The first line of the input contains T, the number of test cases.
The first line of each test case contains N and K. The second line of each test case contains N integers of the array V.

Output:

For each test case, output a single number denoting the summation of time taken to move from each key i to the closest next playable key after i.

Constraints:

• 1 <= T <= 10
• 1 <= N <= 2 * 10⁵
• 1 <= K,V[i] <= N