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 <queue>
using namespace std;
int main(){
    int n,k,top=1<<30,now=0,temp,f[100010];
    queue<int> q;
    scanf("%d%d",&n,&k);
    for(int i=0;i<=k;i++)f[i]=0;
    for(int i=0;i<n;i++){
        scanf("%d",&temp);
        if(temp<=k){
            if(f[temp]==0)now++;
            f[temp]++;
            q.push(temp);
            while(q.front()>k)q.pop();
            while(f[q.front()]>1){
                f[q.front()]--;
                q.pop();
                while(q.front()>k)q.pop();
            }
            if(now==k)if(q.size()<top)top=(int)q.size();
        }
        else q.push(temp);
        //printf("%d\n",q.size());
    }
    if(top==(1<<30))printf("0\n");
    else printf("%d\n",top);
}