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 lint = long long int;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T> void assign(V<T>& v, int n, const T& a = T()) { v.assign(n, a); }
template<class T, class... Args> void assign(V<T>& v, int n, const Args&... args) { v.resize(n); for (auto&& e : v) assign(e, args...); }


int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);
  int n, k; cin >> n >> k;
  V<> a(n); for (int i = 0; i < n; ++i) cin >> a[i], --a[i];
  int res = 1e9;
  V<> c(k);
  int s = 0, r = 0;
  for (int l = 0; l < n; ++l) {
    while (s < k and r < n) {
      if (a[r] < k) s += ++c[a[r]] == 1;
      ++r;
    }
    if (s == k) res = min(res, r - l);
    if (a[l] < k) s -= !--c[a[l]];
  }
  cout << (res != 1e9 ? res : 0) << '\n';
}