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;
using i64 = int64_t;
using vi = vector<i64>;
using vvi = vector<vi>;

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

    set<int> s;
    multiset<int> ss;
    int l = 0, r = 0;
    int minwidth = 1e9;
    while (1) {
        if (s.size() < k) {
            if (r == n) break;
            if (as[r] <= k) {
                ss.insert(as[r]);
                s.insert(as[r]);
            }
            r++;
            continue;
        }
        minwidth = min(minwidth, r - l);
        if (ss.find(as[l]) != ss.end()) {
            ss.erase(ss.find(as[l]));
            if (ss.find(as[l]) == ss.end()) {
                s.erase(as[l]);
            }
        }
        l++;
    }
    cout << (minwidth == 1e9 ? 0 : minwidth) << endl;
}