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;

int main(){
	int n,K;
	cin>>n>>K;
	vector<int> v(n);
	for(int i=0;i<n;i++){
		cin>>v[i],v[i]--;
	}
	vector<int> cnt(100100);
	int c = 0;
	int p = 0;
	int ans = 1e9;
	for(int i=0;i<n;i++){
		while(p<n&&c<K){
			if(v[p]<K){
				cnt[v[p]]++;
				if(cnt[v[p]]==1) c++;
			}
			p++;
		}
		if(c==K){
			ans = min(ans, p-i);
		}
		if(v[i]<K){
			cnt[v[i]]--;
			if(!cnt[v[i]]) c--;
		}

	}
	cout<<(ans==1e9?0:ans)<<endl;
}