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<bits/stdc++.h>
using namespace std;
using ll = long long;

int main()
{
	int n,k;
	cin >> n >> k;
	vector<int> a(n);
	for(int i =0 ;i<n;i++)cin >> a[i];
	vector<int> col(k+1);
	int sum = 0;
	queue<int> Q;
	int ans = n+1;
	for(int i = 0;i<n;)
	{
		//cout<<sum<<';'<<i<<endl;
		if(sum<k)
		{
			if(a[i]<=k&&col[a[i]]==0)
			{
				
				sum++;
			}
			Q.push(a[i]);
			if(a[i]<=k)col[a[i]]++;
			i++;
		}
		else
		{
			//cout<<i<<endl;
			ans = min(ans,(int)Q.size());
			int x = Q.front();
			if(x<=k)
			{
				col[x]--;
				if(col[x]==0)sum--;
			}
			Q.pop();
		}
	}
	while(sum==k)
	{
		ans = min(ans,(int)Q.size());
		int x = Q.front();
		if(x<=k)
		{
			col[x]--;
			if(col[x]==0)sum--;
		}
		Q.pop();
	}
	cout<<(ans==n+1?0:ans)<<endl;

}