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>
using namespace std;
int v[100005], b[100005] = { 0 };
int main() {
	int N, K, R = 0, k = 0;
	scanf("%d%d", &N, &K);
	for (int i = 0; i < N; i++) scanf("%d", &v[i]);
	int start = 0, stop = 0;
	for (;;) {
		for (; stop < N && k < K; stop++) {
			if (v[stop] <= K && ++b[v[stop]] == 1)k++;
		}
		if (k < K) break;
		for (; start < N && k >= K; start++) {
			if (!R || R > stop - start)R = stop - start;
			if (v[start] <= K && !--b[v[start]]) k--;
		}
	}
	printf("%d\n", R);
}