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;
typedef long long ll;

int main() {
    int n, k; cin >> n >> k;
    vector<int> a(n);
    vector<int> cnt(k);
    int rest = k;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    if (k == 1) {
        if (find(a.begin(), a.end(), 1) != a.end()) puts("1");
        else puts("0");
        return 0;
    }
    int l = 0, r = 0;
    constexpr int INF = 1e9 + 6;
    int ans = INF;
    while (r < n) {
        if (a[r] <= k) {
            if (cnt[a[r] - 1] == 0) {
                rest--;
                while (rest == 0) {
                    ans = min(ans, r - l + 1);
                    if (a[l] <= k) {
                        cnt[a[l] - 1]--;
                        if (cnt[a[l] - 1] == 0) {
                            rest++;
                        }
                    }
                    l++;
                }
            }
            cnt[a[r] - 1]++;
        }
        r++;
    }
    if (ans == INF) puts("0");
    else cout << ans << endl;
    return 0;
}