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;
typedef long long ll;
#define REP(i,n) FOR(i,0,n)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define PB push_back
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
const ll INF = (1ll << 60);
typedef pair<ll,ll> pii;

int main(){
  ll N,K; cin>>N>>K;
  vi a(N); REP(i,N) cin>>a[i];
  ll appearingNum=0; vi times(K+1);
  ll l=0,r=0;
  ll ans=INF;
  while(r<N){
    while(appearingNum<K&&r<N){
      if(a[r]<=K){
        if(times[a[r]]==0) appearingNum+=1;
        times[a[r]]+=1;
      }
      r++;
    }
    while(appearingNum==K){
      ans=min(ans,r-l);
      if(a[l]<=K){
        if(times[a[l]]==1) appearingNum-=1;
        times[a[l]]-=1;
      }
      l++;
    }
  }
  if(ans==INF) ans=0;
  cout<<ans<<endl;
}