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 <set>
#include <map>
#include <list>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <cstdio>
#include <vector>
#include <string>
#include <bitset>
#include <cctype>
#include <cstdlib>
#include <cstring>
#include <utility>
#include <numeric>
#include <complex>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <cassert>
#include <iostream>
#include <iterator>
#include <algorithm>
using namespace std;
using ll = long long;
using VL=vector<ll>;

#define REP(i, n) for(int i = 0;i < n;i++)
#define REPR(i, n) for(int i = n;i >= 0;i--)
#define FOR(i, m, n) for(int i = m;i < n;i++)
const long long INF =  999999999;

ll N,K,a[100010],num[100010],cnt=0;
//num[i]は見ている部分列の(i+1)の個数
//a[i]は一個マイナスして0~K-1だけみる
bool flag;


int main(){
  cin>>N>>K;
  REP(i,N){
    cin >>a[i];
    a[i]--;
  }

  ll ans=N+1;
  fill(num,num+N+1,0);
  ll i=0,j=0;
  //[j,i)
  while(true){
    while(cnt <K && i<N){
      if(a[i]<K && a[i]>=0){
        if(num[a[i]]==0)cnt++;
        num[a[i]]++;
      }
      i++;
    }

    while(cnt>=K && j<N){
      ans=min(ans,i-j);
      if(a[j]<K && a[j]>=0){
        if(num[a[j]]-1==0)cnt--;
        num[a[j]]--;
      }
      j++;
    }
    if(i==N)break;
  }

  if(ans==N+1)cout <<0<<endl;
  else cout <<ans<<endl;
}