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;

const int INF = 1e9;

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

  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }

  int l = 0, r = 0;
  int num = 0, ans = INF;
  map<int, int> mp;
  while (l < n) {
    while (r < n && num < k) {
      if (a[r] <= k && mp[a[r]]++ == 0) {
        num++;
      }
      r++;
    }
    if (num < k) break;

    ans = min(ans, r - l);
    if (a[l] <= k && --mp[a[l]] == 0) {
      num--;
    }
    l++;
  }

  cout << ((ans == INF) ? 0 : ans) << endl;

  return 0;
}