Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main()
{
	int i, N, K;
	long long x[51], y[51];
	scanf("%d %d", &N, &K);
	for (i = 1; i <= N; i++) scanf("%lld %lld", &(x[i]), &(y[i]));
	
	int j, k, l, m, count;
	long long X[2], Y[2], min = (long long)1 << 62;
	for (i = 1; i < N; i++) {
		for (j = i + 1; j <= N; j++) {
			X[0] = (x[i] < x[j])? x[i]: x[j];
			X[1] = x[i] + x[j] - X[0];
			for (k = 1; k < N; k++) {
				for (l = k + 1; l <= N; l++) {
					Y[0] = (y[k] < y[l])? y[k]: y[l];
					Y[1] = y[k] + y[l] - Y[0];
					for (m = 1, count = 0; m <= N; m++) if (x[m] >= X[0] && x[m] <= X[1] && y[m] >= Y[0] && y[m] <= Y[1]) count++;
					if (count >= K && (X[1] - X[0]) * (Y[1] - Y[0]) < min) min = (X[1] - X[0]) * (Y[1] - Y[0]);
				}
			}
		}
	}
	
	printf("%lld\n", min);
	fflush(stdout);
	return 0;
}