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 <algorithm>
using namespace std;
int N, K, x[55], y[55];
int main() {
	cin >> N >> K;
	for (int i = 0; i < N; i++) cin >> x[i] >> y[i];
	long long ret = 1LL << 62;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < N; j++) {
			for (int k = 0; k < N; k++) {
				for (int l = 0; l < N; l++) {
					if (x[i] <= x[j] && y[k] <= y[l]) {
						int cnt = 0;
						for (int p = 0; p < N; p++) {
							if (x[i] <= x[p] && x[p] <= x[j] && y[k] <= y[p] && y[p] <= y[l]) cnt++;
						}
						if (cnt >= K) ret = min(ret, 1LL * (x[j] - x[i]) * (y[l] - y[k]));
					}
				}
			}
		}
	}
	cout << ret << endl;
	return 0;
}