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 <iostream>
using namespace std;

#define N 100000
#define INF 1000000
#define MIN(X,Y) ((X)<(Y)?(X):(Y))

int main(void){
  int ans = INF;
  int n, k, l, r, a[N];
  int flg[N+1], cnt;
  
  cin >> n >> k;
  for (int i=0; i<n; i++) cin >> a[i];
  for (int i=1; i<=k; i++) flg[i] = 0;
  cnt = 0;
  l = 0; r = -1;
  while (true){
    while (r<n && cnt < k){
      r++;
      if (a[r]<=k){
        if (flg[a[r]]==0) cnt++;
        flg[a[r]]++;
      }
    }
    if (r==n) break;
    ans = MIN(ans, r-l+1);
//    cout << l << " to " << r << " (" << ans << ")" << endl;
    if (a[l] <= k){
      flg[a[l]]--;
      if (flg[a[l]]==0) cnt--;
    }
    l++;
  }
  cout << (ans==INF?0:ans) << endl;
  return 0;
}