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 PyPy3 (2.4.0) (judge verdict: Accepted)

n, kosuu = map(int, input().split())
XY, X, Y = [], [], []

for _ in range(n):
    x, y = map(int, input().split())
    X.append(x)
    Y.append(y)
    XY.append([x,y])

X = sorted(X, reverse=True)
Y = sorted(Y, reverse=True)

s_min = 10**20
for i in range(n):
    for j in range(n):
        for k in range(n):
            for l in range(n):
                count = 0
                x_max = X[i]
                x_min = X[-1*(j+1)]
                if x_max <= x_min:
                    continue
                y_max = Y[k]
                y_min = Y[-1*(l+1)]
                if y_max <= y_min:
                    continue

                s = abs(x_max-x_min)*abs(y_max-y_min)

                for m in range(n):
                    x = XY[m][0]
                    y = XY[m][1]
                    if (x <= x_max and x >= x_min) and (y <= y_max and y >= y_min):
                        count += 1
                if count >= kosuu:
                    s_min = min(s, s_min)

print(s_min)