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;
#define rep(i,n) for(int i=0;i<(n);i++)

typedef long long ll;
typedef pair<int, int> P;

#define MAX 500005

int main(int, char**)
{
  int n, k;
  cin >> n >> k;

  vector<int> a(n);
  rep(i,n) { cin >> a[i]; --a[i]; }

  int l = 0, r = 0, kind = 0;
  int ans = n + 1;
  map<int, int> count;
  for (;;) {
    while (r < n && kind < k) {
      if (a[r] < k && count[a[r]]++ == 0) kind++;
      r++;
    }
    if (kind < k) break;
    ans = min(ans, r-l);
    if (a[l] < k && --count[a[l]] == 0) kind--;
    l++;
  }
  if (ans > n) ans = 0;
  cout << ans << endl;

  return 0;
}