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 <iostream>
using namespace std;

int main() {
    int n,k,cnt = 0,j = 0,len = __INT_MAX__;
    cin >> n >> k;
    int a[n],ans[n],flag[n + 1];
    for(int i = 0;i < n;++i){
        cin >> a[i];
        ans[i] = flag[i] = 0;
    }
    flag[n] = 0;
    
    for(int i = 0;i < n;++i){
        flag[a[i]]++;
        if(flag[a[i]] == 1 && a[i] <= k){
            cnt++;
        }
        if(cnt < k){
            ans[i] = 0;
        }else{
            while(flag[a[j]] >= 2 || a[j] > k){
                flag[a[j]]--;
                j++;
            }
            ans[i] = i - j + 1;
        }
    }
    
    for(int i = 0;i < n;++i){
        if(ans[i] != 0){
            len = min(len, ans[i]);
        }
    }
    if(len == __INT_MAX__){
        len = 0;
    }
    cout << len << endl;
}