Rikka with Competition

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

A wrestling match will be held tomorrow. $n$ players will take part in it. The $i$th player’s strength point is $a_i$.

If there is a match between the $i$th player plays and the $j$th player, the result will be related to $|a_i-a_j|$. If $|a_i-a_j| > K$, the player with the higher strength point will win. Otherwise each player will have a chance to win.

The competition rules is a little strange. Each time, the referee will choose two players from all remaining players randomly and hold a match between them. The loser will be be eliminated. After $n-1$ matches, the last player will be the winner.

Now, Yuta shows the numbers $n,K$ and the array $a$ and he wants to know how many players have a chance to win the competition.

It is too difficult for Rikka. Can you help her?  

Input

The first line contains a number $t(1 \leq t \leq 100)$, the number of the testcases. And there are no more than $2$ testcases with $n > 1000$.

For each testcase, the first line contains two numbers $n,K(1 \leq n \leq 10^5, 0 \leq K < 10^9)$.

The second line contains $n$ numbers $a_i(1 \leq a_i \leq 10^9)$.

Output

For each testcase, print a single line with a single number -- the answer.

Sample Input

2 5 3 1 5 9 6 3 5 2 1 5 9 6 3

Sample Output

5 1

Hint

liuyiding

Source

2017 Multi-University Training Contest - Te

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