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;
using ll = long long;

#define rep(i,s,n) for(ll i = (s); i < (n); i++)
#define rep0(i,n) rep(i,0,n)
#define rep1(i,n) rep(i,1,n+1)

#define BR "\n"
#define SP " "

int main() {
  int N, K;
  cin >> N >> K;

  vector<ll> A(N), C(K + 1, 0);

  rep0(i, N) cin >> A[i];

  ll ans = 1e9;
  ll l = 0, r = 0;
  ll cnt = 0;
  rep0(i, N) {
    ll a = A[i];
    if (a > K) continue;

    if (C[a] == 0) cnt++;
    C[a]++;

    if (cnt == K) {
      ans = min(ans, i - l + 1);
      
      while (true) {
        ll al = A[l];
        if (al > K) {
          l++;
          ans = min(ans, i - l + 1);
          continue;
        }
        if (C[al] <= 1) break;
        C[al]--;
        l++;
        ans = min(ans, i - l + 1);
      }
    }
  }

  if (ans == 1e9) ans = 0;
  cout << ans << BR;
  return 0;
}