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<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;

#define max(x, y) ((x)>(y)?(x):(y))
#define min(x, y) ((x)<(y)?(x):(y))


Int dict[108000];
Int supp = 0;
Int n, k;

Int cnt(){return supp;}
void add(Int x){
  if(x > k)return;
  if(dict[x]++ == 0)supp++;
}
void remove(Int x){
  if(x > k)return;
  if(dict[x]-- == 1)supp--;
}

int main(){
  Int res = INF;
  cin >> n >> k;
  vector<Int> a(n);
  for(int i = 0;i < n;i++)cin >> a[i];
  int r = 0;
  for(int i = 0;i < n;i++){
    while(r < n && cnt() < k)add(a[r++]);
    if(cnt() == k)res = min(res, r - i);
    remove(a[i]);
  }
  if(res == INF)res = 0;
  cout << res << endl;  
  return 0;
}