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 <cstdio>
#include <vector>
#include <algorithm>
#include <map>

int main() {
  size_t N, K;
  scanf("%zu %zu", &N, &K);

  std::vector<size_t> a(N);
  for (auto& ai: a) scanf("%zu", &ai);

  std::map<size_t, int> m;
  size_t ir = 0;
  for (; ir < N; ++ir) {
    if (a[ir] <= K) ++m[a[ir]];
    if (m.size() == K) {
      ++ir;
      break;
    }
  }

  if (m.size() < K)
    return puts("0"), 0;

  size_t res = ir;
  for (size_t i = 0; i < N; ++i) {
    if (a[i] <= K) {
      auto it = m.find(a[i]);
      if (--it->second == 0) m.erase(it);
    }
    while (m.size() < K && ir < N) {
      if (a[ir] <= K) ++m[a[ir]];
      ++ir;
    }
    if (m.size() == K) {
      res = std::min(res, ir-(i+1));
    }
  }

  printf("%zu\n", res);
}