Problem: We have N points in a two-dimensional plane.
The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).
Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.
Here, points on the sides of the rectangle are considered to be in the interior.
Find the minimum possible area of such a rectangle.

Constraints

* 2 \leq K \leq N \leq 50
* -10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)
* x_i≠x_j (1 \leq i<j \leq N)
* y_i≠y_j (1 \leq i<j \leq N)
* All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:


N K
x_1 y_1
:
x_{N} y_{N}


Output

Print the minimum possible area of a rectangle that satisfies the condition.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999


Output

3999999996000000001

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
#include <limits>
#include <cmath>

using namespace std;


int main() {
	int N, K;
	cin >> N >> K;

	vector<long long> x(N), y(N);

	for (int i = 0; i < N; i++)
		cin >> x[i] >> y[i];

	long long ans = numeric_limits<long long>::max();

	for (int left = 0; left < N; left++) {
		for (int right = 0; right < N; right++) {
			for (int top = 0; top < N; top++) {
				for (int bottom = 0; bottom < N; bottom++) {

					int cnt = 0;
					for (int i = 0; i < N; i++) {
						if (x[left] <= x[i] && x[i] <= x[right]
							&& y[i] <= y[top] && y[bottom] <= y[i])
							cnt++;
					}
					if (cnt >= K) ans = min(ans, (x[right] - x[left])*(y[top] - y[bottom]));
				}
			}
		}
	}

	cout << ans << endl;

	return 0;
}