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 <math.h>
#include <stdlib.h>
#define llint long long int
#define inf 4000000000000000005

using namespace std;

int N, K;
llint x[55], y[55];

int main(void)
{
	cin >> N >> K;
	for(int i = 0; i < N; i++){
		cin >> x[i] >> y[i];
	}
	
	
	llint ans = inf;
	for(int i = 0; i < N; i++){
		for(int j = 0; j < N; j++){
			if(i >= j) continue;
			
			for(int k = 0; k < N; k++){
				for(int l = 0; l < N; l++){
					if(k >= l) continue;
					
					int pt = 0;
					for(int m = 0; m < N; m++){
						if( (x[i]-x[m]) * (x[j]-x[m]) <= 0 && (y[k]-y[m]) * (y[l]-y[m]) <= 0) pt++;
					}
					
					llint s = (x[i] - x[j])*(y[k] - y[l]);
					if(s < 0) s = -s;
					if(pt >= K) ans = min(ans, s);
					
				}
			}
		}
	}
	
	cout << ans << endl;
	return 0;
}