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>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

int a[100000];
int cnt[200000];

int main(){
	int n,k;scanf("%d%d",&n,&k);
	rep(i,n)scanf("%d",&a[i]);
	int g=0;
	set<int>se;
	int ans=INT_MAX;
	rep(i,n){
		while(g<n&&se.size()<k){
			if(a[g]>k){g++;continue;}
			cnt[a[g]]++;
			se.insert(a[g++]);
		}
		if(se.size()<k)break;
		ans=min(ans,g-i);
		if(a[i]<=k){
			cnt[a[i]]--;
			if(!cnt[a[i]])se.erase(a[i]);
		}
	}
	if(ans==
	INT_MAX)puts("0");
	else cout<<ans<<endl;
}