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 CPP):

Solution:
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#define int long long
using namespace std;
int n, k, a[123456], b[123456];
signed main() {
	cin >> n >> k;
	for (int i = 0; i < n; i++)cin >> a[i];
	int f = 0, l = 0, ans = n + 1, sum = 0;
	while (f < n) {
		while (sum < k && l < n) {
			if (a[l] <= k && b[a[l]] == 0)sum++;
			b[a[l++]]++;
		}
		if (sum < k)break;
		ans = min(ans, l - f);
		if (a[f] <= k && b[a[f]] == 1)sum--;
		b[a[f++]]--;
	}
	if (ans > n)cout << "0\n";
	else cout << ans << endl;
}