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: Wrong Answer)

N, K = map(int, input().split())
P = [tuple(map(int, input().split())) for _ in range(N)]
P.sort()

ans = float('inf')
for i in range(N - 1):
    for j in range(i + 1, N):
        (x1, y1), (x2, y2) = P[i], P[j]
        if x1 > x2:
            x1, x2 = x2, x1
        if y1 > y2:
            y1, y2 = y2, y1
        cnt = 0
        for k in range(i + 1, j):
            x3, y3 = P[k]
            if x1 <= x3 <= x2 and (y1 <= y3 <= y2):
                cnt += 1
        if cnt >= K - 2:
            ans = min(ans, abs((x2 - x1) * (y2 - y1)))

if N >= 3:
    for i in range(N - 2):
        for j in range(i + 1, N - 1):
            for k in range(j + 1, N):
                (xi, yi), (xj, yj), (xk, yk) = P[i], P[j], P[k]
                x1 = min([xi, xj, xk])
                x2 = max([xi, xj, xk])
                y1 = min(([yi, yj, yk]))
                y2 = max(([yi, yj, yk]))
                cnt = 0
                for l in range(i + 1, k):
                    x3, y3 = P[l]
                    if x1 <= x3 <= x2 and (y1 <= y3 <= y2):
                        cnt += 1
                if cnt >= K - 2:
                    ans = min(ans, abs((x2 - x1) * (y2 - y1)))

print(ans)