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 <iostream>
#include <vector>
int main() {
	int n, k;
	std::cin >> n >> k;
	std::vector<int> nums(n);
	std::vector<int> counts(k, 0);
	for (auto &num : nums) {
		std::cin >> num;
	}
	int left{ 0 }, right{ 0 }, count{ 0 };
	int min_length = n + 1;
	while (true) {
		while (count < k && right < n) {
			if (nums[right] <= k && counts[nums[right] - 1]++ == 0) ++count;
			++right;
		}
		if (count == k) {
			while (count == k) {
				if (nums[left] <= k && --counts[nums[left] - 1] == 0) --count;
				++left;
			}
			if (min_length > right - left + 1) min_length = right - left + 1;
		}
		else break;
	}
	if (min_length == n + 1) std::cout << 0 << std::endl;
	else std::cout << min_length << std::endl;
}