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;
typedef long long ll;
#define P pair<int,int>
#define FOR(I,A,B) for(ll I = ll(A); I < ll(B); ++I)


int main(){

	ll N,K,count=0,ans=100001;
	cin >> N >> K;
	vector<ll> a(N),counta(100001,0);
	FOR(i,0,N)cin >> a[i];

	ll l=0,r=1;
	counta[a[0]]++;
	if(1<=a[0] && a[0]<=K)count++;

	FOR(i,0,N){
		while(count<K && r<N){
			counta[a[r]]++;
			if(counta[a[r]]==1 && 1<=a[r] && a[r]<=K)count++;
			r++;
		}
		if(count==K)ans=min(ans,r-l);
		counta[a[l]]--;
		if(counta[a[l]]==0 && 1<=a[l] && a[l]<=K)count--;
		l++;
	}
	if(ans==100001)ans = 0;
	cout << ans << endl;
	
}