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 INF=0x3f3f3f3f;

int n,s,k,ans=INF;
int a[100005],b[100005];

int main() {
    ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    cin>>n>>k; s=k;
    for (int i=0;i<n;++i) cin>>a[i];
    for (int i=0,j=0;j<=n;) {
        if (s>0) {
            if (!b[a[j]] && a[j]<=k) --s;
            ++b[a[j]];
            ++j;
        }
        else {
            ans=min(ans,j-i);
            --b[a[i]];
            if (!b[a[i]] && a[i]<=k) ++s;
            ++i;
        }
    }
    cout<<(ans==INF?0:ans)<<'\n';
}