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: Time Limit Exceeded)

import math
INF = 10000000000000000000000000000000000
N, K = map(int, input().split())
points = []
to_search_x = []
to_search_y = []
for i in range(N):
    xi, yi = map(int, input().split())
    points.append([xi, yi])
    to_search_x.append(xi)
    to_search_y.append(yi)

to_search_x.sort()
to_search_y.sort()

def is_between(x1, x2, x):
    if x >= x1 and x <= x2:
        return True
    elif x <= x1 and x >= x2:
        return True
    else:
        return False

def count(x1, x2, y1, y2):
    num = 0
    for i in range(N):
        if is_between(x1, x2, points[i][0]) and is_between(y1, y2, points[i][1]):
            num += 1
    return num

ans = INF
for i in range(N):
    for j in range(i,N):
        for k in range(N):
            for l in range(k,N):
                if count(to_search_x[i], to_search_x[j], to_search_y[k], to_search_y[l]) >= K:
                    ans = min(ans, abs((to_search_x[i]-to_search_x[j])*(to_search_y[k]-to_search_y[l])))

print(ans)