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 <climits>
#include <iostream>
#include <unordered_map>
#include <vector>
using namespace std;

int main() {
	int N, K, ans = INT_MAX, i = 0;
	cin >> N >> K;
	vector<int> a(N);
	for (int& j : a) cin >> j;
	unordered_map<int, int> b;
	for (int j = 0; j < N; ++j) {
		while (K != b.size() && N != i) {
			if (K >= a[i]) ++b[a[i]];
			++i;
		}
		if (K == b.size()) ans = min(ans, i - j);
		if (i == j) ++i;
		else {
			if (b.end() != b.find(a[j])) {
				--b[a[j]];
				if (!b[a[j]]) b.erase(a[j]);
			}
		}
	}
	if (INT_MAX == ans) ans = 0;
	cout << ans << endl;
}