Card Game

Bob likes playing cards. For his birthday his friend Alice gave him a set of cards.

There are $N$ cards, and each card has one integer written on it. Bob lays the cards on a desk from left to right and wants to discard some of them. Before discarding anything he picks one integer $K$. Each discard takes three cards that are neighbours at that moment. If the numbers on those three cards, read from left to right, are $a$, $b$ and $c$, they must satisfy

$c - b = b - a = K$

Discarding three cards empties their place, so the card just left of them and the card just right of them become neighbours. Bob repeats this as long as some three neighbouring cards satisfy the condition, and he may choose which three to discard.

Find the smallest number of cards Bob can be left with when he chooses discards as well as possible.

The first line contains the number of test cases $T$. $T$ test cases follow.

Each test case has two lines. The first line contains the number of cards $N$ and the number $K$ that Bob picked, separated by a space. The second line contains the numbers on the cards from left to right, $a_1, a_2, \dots, a_N$, separated by spaces.

Limits

• $1 \le T \le 100$
• $1 \le N \le 100$
• $1 \le a_i \le 10^6$ ($1 \le i \le N$)
• $0 \le K \le 10^6$

For each test case, print one line in the form Case #x: y, where $x$ is the test case number starting from 1, and $y$ is the smallest number of cards Bob can be left with.