Problem: 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.

Examples

Input

6 2
4 1 2 1 3 5


Output

2


Input

6 3
4 1 2 1 3 5


Output

3


Input

3 4
1 2 3


Output

0

Solution (in PYTHON3):

Solution:
# -*- coding: utf-8 -*-
"""
Sliding Window - The Smallest Window II
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_3_B&lang=jp

"""
from collections import defaultdict

N, K = map(int, input().split())
A = [int(a) for a in input().split()]

left, right, num = 0, 0, 0
ans = float('inf')
count = defaultdict(int)
while True:
    while right < N and num < K:
        if count[A[right]] == 0 and A[right] <= K:
            num += 1
        count[A[right]] += 1
        right += 1
    if num < K:
        break
    ans = min(ans, right - left)
    if count[A[left]] == 1 and A[left] <= K:
        num -= 1
    count[A[left]] -= 1
    left += 1
print(ans if ans != float('inf') else 0)