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>
using namespace std;

using ll = long long;

#define for_(i,a,b) for(int i = (a);i < (b);i++)
#define rfor_(i,a,b) for(int i = (b)-1;i >= (a);i--)
#define rep(i,n) for_(i,0,(n))
#define rrep(i,n) rfor_(i,0,(n))

const int mx = 100005;

int N, K;

int s, t, l, c;

int a[mx], b[mx];

int main(){
	cin.tie(0);
	
	cin>>N>>K;
	
	rep(i, N)cin>>a[i];
	
	l = N+1;
	
	while(s<N) {
		if(s>0) {
			if(a[s-1]<=K && --b[a[s-1]] == 0)c--;
		}
		while(t<N) {
			if(c==K)break;
			if(a[t]<=K && b[a[t]]++ == 0)c++;
			t++;
		}
		if(c<K)break;
		if(c==K && l>t-s)l = t-s;
		s++;
	}
	
	cout<<(l>N?0:l)<<endl;
	
	return 0;
}