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 Python (3.4.3) (judge verdict: Accepted)

def axis_parallel_rectangle(N: int, K: int, xy: list)->int:
    # 1. 座標圧縮
    sorted_x = sorted(v[0] for v in xy)
    sorted_y = sorted(v[1] for v in xy)

    XY = [(sorted_x.index(v[0]), sorted_y.index(v[1])) for v in xy]
    # 2. 圧縮された座標上で点の個数に関して累積和をとる。
    S = [[0] * (N+1) for _ in range(N+1)]
    for x, y in XY:
        S[x+1][y+1] = 1

    for x in range(N+1):
        for y in range(N):
            S[x][y+1] += S[x][y]

    for y in range(N+1):
        for x in range(N):
            S[x+1][y] += S[x][y]

    # 3. x 座標から二つを選ぶ。
    min_area = float('inf')
    for x1 in range(N):
        for x2 in range(x1+1, N):
            for y1 in range(N):
                for y2 in range(y1+1, N):
                    count = S[x2+1][y2+1]-S[x2+1][y1]-S[x1][y2+1]+S[x1][y1]
                    if count < K:
                        continue
                    xmin, xmax = sorted_x[x1], sorted_x[x2]
                    ymin, ymax = sorted_y[y1], sorted_y[y2]
                    min_area = min(min_area, (xmax-xmin)*(ymax-ymin))
    # これで O(N^3) = O(10^5) くらい ?
    return min_area


if __name__ == "__main__":
    N = 0
    N, K = map(int, input().split())
    xy = [tuple(map(int, input().split())) for _ in range(N)]
    ans = axis_parallel_rectangle(N, K, xy)
    print(ans)