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 = 1e9;

int main() {
    int n, k;
    cin >> n >> k;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        if (a[i] > k) a[i] = 0;
    }

    int ans = INF;
    map<int, int> mp;
    for (int l = 0, r = 0; l < n; l++) {
        while (r < n and mp.size() < k) {
            if (a[r] > 0) mp[a[r]]++;
            r++;
        }
        if (mp.size() == k) {
            ans = min(ans, r - l);
        }
        if (a[l] > 0) {
            if (--mp[a[l]] == 0) mp.erase(a[l]);
        }
    }

    if (ans == INF) ans = 0;
    cout << ans << '\n';

    return 0;
}