Exhibition Brilliance

You are given n paintings arranged in a row. The i-th painting has a main pigment type denoted by a_i. You can select a contiguous segment of these paintings to form an exhibition. Let the chosen segment be from index l to r, and for each pigment type i (with i=1,2,...,W where W is the total number of possible pigment types), let c_i denote the number of paintings in the segment whose pigment is type i.

The brilliance of the exhibition is defined as

Your task is to determine the minimum length of a contiguous segment such that its brilliance is at least k. If no such segment exists, output -1.

Note: If a pigment type does not appear in the segment, then its count is zero.

inputFormat

The first line contains two integers n and k (1 ≤ n ≤ 10⁵, 0 ≤ k ≤ 10¹²), representing the number of paintings and the required minimum brilliance, respectively.

The second line contains n integers a1, a2, ..., an (1 ≤ a_i ≤ 10⁹), where ai denotes the pigment type of the i-th painting.

outputFormat

Output a single integer representing the minimum number of consecutive paintings required for an exhibition with brilliance at least k. If no valid exhibition exists, output -1.

sample

5 4
1 2 2 1 3

5