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<vector>
#include<algorithm>
using namespace std;
static const int INF = 1 << 30;

int main(){
	int N, K;
	cin >> N >> K;
	vector<int> a(N);
	for(int i = 0; i < N; i++){
		cin >> a[i];
		a[i]--;
	}
	vector<int> num(K, 0);
	int res = INF;
	int cnt = 0;
	int j = 0;
	for(int i = 0; i < N; i++){
		for(; j < N; j++){
			if(cnt >= K) break;
			if(a[j] < K){
				if(num[a[j]] == 0) cnt++;
				num[a[j]]++;
			}
		}
		if(cnt >= K){
			res = min(res, j - i);
		}
		if(a[i] < K){
			num[a[i]]--;
			if(num[a[i]] == 0) cnt--;
		}
	}
	cout << (res == INF ? 0 : res) << endl;
	return 0;
}