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 <iostream>
#include <map>
using namespace std;

int main() {
  int A[100005];
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; ++i)
    cin >> A[i];
  map<int, int> cts;
  int values_in_window = 0;
  int m = 100005;
  for (int f = 0, b = 0; f < n; ++f) {
    if (!cts[A[f]] and A[f] <= k)
      ++values_in_window;
    cts[A[f]] += 1;
    while (A[b] > k or cts[A[b]] > 1)
      cts[A[b++]]--;
    if (values_in_window >= k)
      m = min(m, f - b + 1);
  }
  cout << (m > 1e5 ? 0 : m) << endl;
}