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 N=1e5+10;
const int INF=1e9+10;
int a[N];

bool in(int a,int b)
{
    return a>0&&a<=b;
}

int main()
{
    int n,k;

    ios::sync_with_stdio(false);
    cin.tie(0);

    while(cin>>n>>k)
    {
        for(int i=0;i<n;i++)
        {
            cin>>a[i];
        }

        map<int,int> mp;
        int Min=INF;
        int cnt=0;

        for(int l=0,r=0;l<n;l++)
        {
            while(r<n&&cnt<k)
            {
                if(mp[a[r++]]++==0&&in(a[r-1],k))
                {
                    cnt++;
                }
            }
            if(cnt==k)
            {
                Min=min(Min,r-l);
            }
            if(in(a[l],k)&&mp[a[l]]--==1)
            {
                cnt--;
            }
        }
        if(Min==INF) Min=0;
        cout<<Min<<endl;
    }

    return 0;
}