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>
#include <vector>
#include <algorithm>

using namespace std;

int main() {
    int n, k;
    cin >> n >> k;
    vector<int> counts(k + 1, 0);
    vector<int> v(n);
    
    for (int i = 0; i < n; i++) {
        cin >> v[i];
    }
    
    int total = 0;
    
    int ans = 1000000000;
    for (int l = 0, r = 0; r < n; r++) {
        if (v[r] > k) {
            continue;
        } 
        counts[v[r]]++;
        if (counts[v[r]] == 1) {
            total++;
        }
        while (l < r && (v[l] > k || (total == k && counts[v[l]] > 1))) {
            if (v[l] <= k) {
                counts[v[l]]--;
            }
            l++;
        }
        if (total == k) {
            ans = min(ans, r - l + 1);
        }
        
    }
    
    cout << (total == k? ans : 0) << endl;
    
    
    return 0;
}