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 "bits/stdc++.h"
#define in std::cin
#define out std::cout
#define rep(i,N) for(int i=0;i<N;++i)
typedef long long int LL;

const LL inf = 1123456789;
LL N, K, cou, ans;

int main()
{
	in >> N >> K;
	std::vector<LL>x(N), y(N);
	rep(i, N) in >> x[i] >> y[i];
	ans = 4123456789012345678;
	rep(i, N)
	{
		rep(j, N)
		{
			rep(k, N)
			{
				rep(l, N)
				{
					LL minX = std::min({ x[i],x[j],x[k],x[l] });
					LL maxX = std::max({ x[i],x[j],x[k],x[l] });
					LL minY = std::min({ y[i],y[j],y[k],y[l] });
					LL maxY = std::max({ y[i],y[j],y[k],y[l] });
					cou = 0;
					rep(m, N)
					{
						if (minX <= x[m] && x[m] <= maxX && minY <= y[m] && y[m] <= maxY) ++cou;
					}
					if (cou >= K) ans = std::min(ans, (maxX - minX)*(maxY - minY));
				}
			}
		}
	}
	out << ans << std::endl;
	return 0;
}