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<cstdio>
#include<algorithm>
#include<map>
#include<string>
#include<vector>
#include<climits>

#define MAX 100001

int n,k;
int a[MAX];

using namespace std;

void solve(){
	int ans=n+1;
	int l=0,r=0;
	map<int,int> m;
	while(1){
		while(r<n&&m.size()<k){
			if(a[r]<=k) m[a[r]]++;
			r++;
		}
		if(m.size()<k) break;
		ans=min(ans,r-l);
		if(a[l]<=k){
			if(m[a[l]]==1) m.erase(a[l]);
			else m[a[l]]--;
		}
		l++;
	}
	if(ans>n) ans=0;
	printf("%d\n",ans);
}

int main(){
	scanf("%d %d",&n,&k);
	for(int i=0;i<n;i++) scanf("%d",&a[i]);
	solve();
}