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>
using namespace std;
int n,k,cnt[1<<17],ans=1e9,now,a[1<<17],f;
int main()
{
	cin>>n>>k;
	for(int i=0;i<n;i++)
	{
		cin>>a[i];
		if(a[i]<=k)now+=!cnt[a[i]];
		cnt[a[i]]++;
		while(f<i&&(a[f]>k||cnt[a[f]]>1))cnt[a[f++]]--;
		if(now==k)ans=min(ans,i-f+1);
	}
	cout<<(ans==1e9?0:ans)<<endl;
}