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:
#define _USE_MATH_DEFINES
#define _CRT_SECURE_NO_WARNINGS

#include <iostream>
#include <string>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <stack>
#include <queue>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <bitset>
#include <utility>
#include <numeric>

using namespace std;

using ll = long long;
using ull = unsigned long long;

const ll inf = (ll)1e9;
const ll mod = (ll)1e9 + 7;

int main()
{
	int n, k;
	cin >> n >> k;

	vector<int> a(n);
	for (int i = 0; i < n; i++)
	{
		cin >> a.at(i);
	}

	map<int, int> m;

	int r = 0;
	int ans = inf;
	for (int l = 0; l < n; l++)
	{
		while (r < n && m.size() < k)
		{
			if (a.at(r) <= k)
			{
				m[a.at(r)]++;
			}
			r++;
		}

		if (m.size() == k)
		{
			ans = min(ans, r - l);
		}

		if (l == r)
		{
			r++;
		}
		else
		{
			if (a.at(l) <= k)
			{
				m[a.at(l)]--;
				if (m[a.at(l)] == 0)
				{
					m.erase(a.at(l));
				}
			}
		}
	}

	if (ans == (int)inf)
	{
		ans = 0;
	}

	cout << ans << endl;
}