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;

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> cnt(K);
        int num=0, ans=N+1;
        for(int l=0, r=0;l<N;l++){
                while(r<N and num<K){
                        if(a[r]<K){
                                if(++cnt[a[r]]==1) num++;
                        }
                        r++;
                }
                if(num<K) break;
                ans=min(ans, r-l);
                if(a[l]<K) if(--cnt[a[l]]==0) num--;
        }
        cout<<(ans==N+1? 0:ans)<<endl;
        return 0;
}