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;

#define int long long
#define endl '\n'
#define MOD 1000000007
#define maxn 100010

void solve() {
    int n, k;
    cin >> n >> k;

    vector<int> v(n);
    map<int, int> mp;
    for (int i = 0; i < n; i++)
        cin >> v[i];
    int ct = 0, ans = n + 10;
    for (int j = 0, i = 0; i < n and j < n; i++) {
        mp[v[i]]++;
        if (mp[v[i]] == 1 and v[i] <= k)
            ct++;
        while (ct >= k and j < n and (mp[v[j]] - 1 >= 1 or v[j] > k) and j < i) {
            mp[v[j]]--;
            j++;
        }
        if (ct >= k)
            ans = min(ans, i - j + 1);
    }
    if (ans == n + 10)
        ans = 0;
    cout << ans << endl;
}

int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int t = 1;
//    cin >> t;

    while (t--)
        solve();
    return 0;
}