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>
using namespace std;

long long N, K;
long long x[55];
long long y[55];
long long ans;


long long func(long long x1, long long y1, long long x2, long long y2){
	long long tmp = 0;
	long long minix = min(x1, x2);
	long long maxix = max(x1, x2);
	long long miniy = min(y1, y2);
	long long maxiy = max(y1, y2);

	for(long long i = 0; i < N; i++){
		if(minix <= x[i] && x[i] <= maxix)
			if(miniy <= y[i] && y[i] <= maxiy)
				tmp++;
	}
	if(tmp >= K)
		ans = min(ans, (maxix - minix) * (maxiy - miniy));
}

int main(){
	cin >> N >> K;
	for(long long i = 0; i < N; i++){
		cin >> x[i] >> y[i];
	}

	ans = LONG_MAX;
	for(long long i = 0; i < N; i++)
		for(long long j = 0; j < N; j++)
			for(long long k = 0; k < N; k++)
				for(long long l = 0; l < N; l++)
					func(x[i], y[j], x[k], y[l]);
	cout << ans << endl;
}