Problem:
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The Smallest Window II

For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $K$, find the smallest sub-array size (smallest window length) where the elements in the sub-array contains all integers in range [$1, 2, ..., K$]. If there is no such sub-array, report 0.

Constraints

$1 \leq N \leq 10^5$

$1 \leq K \leq 10^5$

$1 \leq a_i \leq 10^5$

Input

The input is given in the following format.

$N$ $K$

$a_1$ $a_2$ ... $a_N$

Output

Print the smallest sub-array size in a line.

Sample Input 1

6 2
4 1 2 1 3 5

Sample Output 1

2

Sample Input 2

6 3
4 1 2 1 3 5

Sample Output 2

3

Sample Input 3

3 4
1 2 3

Sample Output 3

0

Solution in Ruby (judge verdict: Accepted)

n, k = gets.chomp.split.map(&:to_i)
arr = gets.chomp.split.map(&:to_i)
h = Hash.new(0)
l = r = 0
li = ri = -1
zero, min = k, nil
while true
    if 1 <= r && r <= k
        h[r] += 1
        zero -= 1 if h[r] == 1
    end
    if 1 <= l && l <= k
        h[l] -= 1
        zero += 1 if h[l] == 0
    end
    if zero == 0
        min = ri - li if min.nil? || min > ri - li
        li += 1
        break if li == ri
        l, r = arr[li], 0
    else
        ri += 1
        break if ri == n
        l, r = 0, arr[ri]
    end
end
puts (min.nil? ? 0 : min)