Alice lives in a country. In this country, there are only $N$ cities located in a row, each city has a magic number such as the $i^{th}$ city contains $a_i$ number. She wants to visit the $K$ cities of this country. Alice starts with a city where the magic number of that city is $1$. Then if you are in city $X$, then the next city can be city $Y$, if $a_y = a_x + 1$. Alice wants to choose the order of the cities she will visit so that the distance traveled was the maximum. The distance between neighboring cities is $1$.

Input format

• The first line is the number $T$ denoting the number of tests.
• The first line of each test contains two integers $N$ and $K$ denoting the number of cities in the country and the number of cities Alice wants to visit.
• The second line contains $N$ integers $a_i$ denoting magic numbers for each city.

Output format

In a single line, print one integer denoting the maximum distance that Alice will have to cover.

Constraints

$1 ≤  T ≤  10$
$1 ≤  K ≤  N ≤  10^5$
$1≤  a_i ≤  K$

For each $j$, there is at least a city with the magic number $j (1≤ j ≤  K)$.