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 <stdio.h>
#include <cmath>
#include <algorithm>
#include <cfloat>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <iostream>
#include <set>
#include <map>
#include <time.h>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;


#define NUM 100000

int main(){

	int N,K;
	scanf("%d %d",&N,&K);

	int* table = new int[N];
	for(int i = 0; i < N; i++)scanf("%d",&table[i]);

	int* check = new int[NUM+1];
	for(int i = 1; i <= NUM; i++)check[i] = 0;

	int count = 0,left = 0,right = 0;
	int ans = BIG_NUM;

	while(true){

		while(right <= N-1){
			check[table[right]]++;
			if(table[right] <= K && check[table[right]] == 1){
				count++;
			}
			if(count == K)break;
			right++;
		}
		if(right == N)break;

		ans = min(ans,right-left+1);

		while(left <= right){
			left++;
			check[table[left-1]]--;
			if(table[left-1] <= K && check[table[left-1]] == 0){
				count--;
				break;
			}
			ans = min(ans,right-left+1);
		}
		right++;
	}

	if(ans == BIG_NUM){
		printf("0\n");
	}else{
		printf("%d\n",ans);
	}

	return 0;
}