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;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pairInt;
typedef tuple<int, int, int> tuple3Int;
#define FOR(i, n) for (int i = 0; i < int(n); i++)
#define FOR1(i, m, n) for (int i = int(m); i < int(n); i++)
#define MAX(a, b) ((a) >= (b) ? (a) : (b))
#define MIN(a, b) ((a) <= (b) ? (a) : (b))

int main(int argc, char *argv[])
{
  int N, K;
  vector<int> a;

  scanf("%d%d", &N, &K);
  a.resize(N);

  FOR(i, N) scanf("%d", &a[i]);

  map<int, int> m;
  int sum(0), l(0), r(0), ans(INT_MAX);
  while (r < N) {
    while (r < N && m.size() < K) {
      if (a[r] > K) {
        r++;
        continue;
      }
      m[a[r++]]++;
    }
    if (m.size() < K) break;
    while (m.size() >= K){
      if (a[l] > K) {
        l++;
        continue;
      }
      auto it = m.find(a[l]);
      if (it->second == 1)
        m.erase(it);
      else
        it->second--;
      l++;
    }
    if (r - l + 1 < ans) ans = r - l + 1;
  }

  printf("%d\n", ans == INT_MAX ? 0 : ans);
  
  return 0;
}