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;
const int inf = 1e9;

int a[100002], b[100002];
int main(){
	int n, k, ans = inf;
	scanf("%d%d", &n, &k);
	for(int i = 1;i <= n;i++)scanf("%d", &a[i]);
	
	int l = 0, r = 0, sum = 0;
	while(r <= n){
		if(r == n && sum < k)break;
		if(sum == k)ans = min(ans, r-l);
		if(sum < k){if(a[++r] <= k && b[a[r]]++ == 0)sum++;}
		else {if(a[++l] <= k && --b[a[l]] == 0)sum--;}
	}
	
	if(ans == inf)printf("0\n");
	else printf("%d\n", ans);
	return 0;
}