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;

void solve()
{
    int n, k;
    cin >> n >> k;
    vector<int> as(n);
    for (int i = 0; i < n; i++)
    {
        cin >> as[i];
    }
    int ans = n + 1, r = -1, cnt = 0;
    vector<int> bincnt(k + 1);
    for (int l = 0; l <= n - k; l++)
    {
        while (r < l || (cnt < k && r + 1 < n))
        {
            if (1 <= as[r + 1] && as[r + 1] <= k)
            {
                if (!bincnt[as[r + 1]])
                {
                    cnt++;
                }
                bincnt[as[r + 1]]++;
            }
            r++;
        }
        //cout << l << ' ' << r << endl;
        if (cnt == k)
        {
            ans = min(ans, r - l + 1);
        }
        if (1 <= as[l] && as[l] <= k)
        {
            if (--bincnt[as[l]] == 0)
            {
                cnt--;
            }
        }
    }
    if (ans == n + 1)
    {
        ans = 0;
    }
    cout << ans << endl;
}

int main()
{
    solve();
    return 0;
}