Aoki has a shuffled deck of cards which is a permutation of 1 to N. He wants to show off an impressive trick to his friends - dealing many cards in decreasing order!
However, Aoki only skilled enough to deal one of the top K cards of the deck. What is the longest sequence of cards of decreasing number he can deal?
The first line of input will contain two integers, N and K.
The next line contain N integers, which respresent the deck. The first integer is the card that is on the top of the deck. Each number is between 1 to N inclusive, and no two numbers are the same.
The output should contain one integer, the maximum number of cards Aoki can deal.
For all subtasks: 1 ≤ K ≤ N ≤ 500 000.
Subtask 1 (30%): K = 2.
Subtask 2 (70%): No additional constraints.
Subtask 3 (0%): Sample.
6 2 2 5 4 1 6 3
He can deal the cards 5, 4, 2, 1 in this order. After this, there is no card smaller than 1, so it's impossible.