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 <algorithm>
#include <cstdio>
#include <iostream>
#include <map>
#include <cmath>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
#include <stdlib.h>
#include <stdio.h>
#include <bitset>
#include <cstring>
#include <deque>
#include <iomanip>
#include <limits>
#include <fstream>
using namespace std;
#define FOR(I,A,B) for(int I = (A); I < (B); ++I)
#define CLR(mat) memset(mat, 0, sizeof(mat))
typedef long long ll;

int main()
{
  ios::sync_with_stdio(false);
  cin.tie(0);
  int N, K;
  cin >> N >> K;
  int a[N];
  FOR(i,0,N) cin >> a[i];
  int ans = 1e9;
  int r = 0;
  map<int, int> mp;
  // [l, r)の和をみる
  FOR(l,0,N) {
    while(r < N && mp.size() < K) {
      if(a[r] <= K) mp[a[r]]++;
      r++;
    }
    if(mp.size() == K) ans = min(ans, r - l);
    if(a[l] <= K) {
      mp[a[l]]--;
      if(mp[a[l]] == 0) {
        mp.erase(a[l]);
      }
    }
  }
  cout << (ans != 1e9 ? ans : 0) << endl;
}