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;

signed main(){

  int n,k;
  cin>>n>>k;
  vector<int> a(n);
  for(auto& ai:a)cin>>ai;

  int ans = n+1;
  int l=0,r=0;
  set<int> st;
  map<int,int> mp;
  for(;l<n;++l){
    bool f = (r<n)&&(st.size()!=k);
    while(f){
      if(a[r]<=k)st.emplace(a[r]);
      mp[a[r]]++;
      r++;
      f = (r<n)&&(st.size()!=k);
    }
    if(st.size()==k){
      ans = min(ans,r-l);
    }
    mp[a[l]]--;
    if(mp[a[l]]==0)st.erase(a[l]);
  }
  cout<<(ans==n+1?0:ans)<<endl;

}