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;

int n, k, uniq = 0, a[100005];
bool has1[100005];
int freq[100005];

int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    has1[a[i]] = true;
  }
  for (int i = 1; i <= k; i++) {
    if (!has1[i]) {
      cout << 0 << endl;
      return 0;
    }
  }
  int l = 1, r = 0;
  while (uniq != k) {
    freq[a[++r]]++;
    if (a[r] <= k && freq[a[r]] == 1) {
      uniq++;
    }
  }
  int ans = r - l + 1;
  while (r <= n) {
    // shrink left bound
    if (uniq == k)
      while (a[l] > k || freq[a[l]] > 1)
	freq[a[l++]]--;
    if (uniq == k)
      ans = min(ans, r - l + 1);
    freq[a[++r]]++;
    if (a[r] <= k && freq[a[r]] == 1)
      uniq++;
    if (a[l] <= k && freq[a[l]] == 1)
      uniq--;
    freq[a[l++]]--;
  }
  cout << ans << endl;
}