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;

template< class T >
int slide_smallest2(const vector<T>& v, T k) {
    map<T, int> m;
    int l=0, r;
    int ret = v.size() + 1;
    for (r = 0; r < v.size(); ++r) {
        if (v[r] > k) continue;
        m[v[r]] = r;
        while (m.size() == k) {
            ret = min(ret, r - l + 1);
            if (v[l] <= k && m[v[l]] == l) m.erase(v[l]);
            l++;
        }
    }
    if (ret == v.size() + 1) return 0;
    return ret;
}

int main() {
    int N, K;
    cin >> N >> K;
    vector<int> v(N);
    for (int i = 0; i < N; ++i) {
        cin >> v[i];
    }
    cout << slide_smallest2(v, K) << endl;
}