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;

const int INF = 1 << 30;

int N, K, A[100000];
int exist[100001], sum;

int main() {
  cin >> N >> K;
  for(int i = 0; i < N; i++) cin >> A[i];
  int ret = INF, tail = 0;


  for(int i = 0; i < N; i++) {
    while(tail < N && sum < K) {
      sum += exist[A[tail]]++ == 0 && A[tail] <= K;
      ++tail;
    }
    if(sum == K) ret = min(ret, tail - i);
    sum -= exist[A[i]]-- == 1 && A[i] <= K;
  }
  printf("%d\n", ret == INF ? 0 : ret);
}