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 <cstdio>
#include <vector>
using namespace std;
int main(){
	int N,K,R=0,k=0;
	scanf("%d%d",&N,&K);
	vector<int>v(N),b(K+1);
	for(int i=0;i<N;i++)scanf("%d",&v[i]);
	int start=0,stop=0;
	for(;;){
		for(;stop<N&&k<K;stop++){
			if(v[stop]<=K&&++b[v[stop]]==1)k++;
		}
		if(k<K)break;
		for(;start<N&&k>=K;start++){
			if(!R||R>stop-start)R=stop-start;
			if(v[start]<=K&&!--b[v[start]])k--;
		}
	}
	printf("%d\n",R);
}