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 \(j (1≤ j ≤  K) \).