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;
#define rep(i,n) for(int i=0;i<n;i++)
int n, K, x[55], y[55];
long long ans = 1e18 * 4;
int main() {
	cin >> n >> K;
	rep(i, n)cin >> x[i] >> y[i];
	rep(i, n) {
		rep(j, n) {
			rep(k, n) {
				rep(l, n) {
					int cnt = 0;
					rep(m, n)if (min(x[i], x[j]) <= x[m] && max(x[i], x[j]) >= x[m] && min(y[k], y[l]) <= y[m] && max(y[k], y[l]) >= y[m])cnt++;
					if (cnt >= K)ans = min(ans, (long long)abs(x[i] - x[j])*abs(y[k] - y[l]));
				}
			}
		}
	}
	cout << ans << endl;
	getchar();getchar();
}