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 rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;
const int INF = 1e9;

int main(){
  int n, k;
  cin >> n >> k;
  int a[n];
  rep(i,n) cin >> a[i];
  int l = 0;
  vector<int> u(n+1);
  int num = 0;
  int r = 0;
  int ans = INF;
  rep(l,n) {
    while(r < n && num < k) {
      if(u[a[r]] == 0 && a[r] <= k) num++;
      u[a[r]]++;
      r++;
    }
    if(num == k) ans = min(ans,r-l);
    if(u[a[l]] == 1 && a[l] <= k) num--;
    u[a[l]]--;
  }
  cout << (ans == INF ? 0 : ans) << endl;
  return 0;
}