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 int long long
signed main(){
  int n,k;
  cin>>n>>k;
  int a[n];
  for(int i=0;i<n;i++) cin>>a[i];
  int ans=n+1;
  int x[k];
  memset(x,0,sizeof(x));
  int cnt=0;
  int l=0;
  for(int i=0;i<n;i++){
    //cout<<i<<" "<<a[i]<<":"<<cnt<<endl;
    a[i]--;
    if(a[i]>=k) continue;
    x[a[i]]++;
    if(x[a[i]]==1) cnt++;
    while(cnt==k){
      if(a[l]>=k){
	l++;
	continue;
      }
      ans=min(ans,i-l+1);
      x[a[l]]--;
      if(x[a[l]]==0) cnt--;
      l++;
    }
  }
  if(ans>n) ans=0;
  cout<<ans<<endl;
  return 0;
}