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)

N, K = map(int, input().split())

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

dots = XY[:]

import sys
INT_MAX = sys.maxsize

x_dots = [(x, y) for x, y in dots]
x_dots = sorted(x_dots)
y_dots = [(x, y) for x, y in dots]
y_dots = sorted(y_dots, key=lambda x: x[1])

ans = INT_MAX
for l in range(N):
    for r in range(l+1, N+1):
        for u in range(N):
            for t in range(u+1, N+1):
                xy_dots =  set(x_dots[l:r]) & set(y_dots[u:t])
                if len(xy_dots) >= K:
                    #print("---")
                    #print(l, r, x_dots[l:r])
                    #print(u, t, y_dots[u:t])
                    #print(x_dots[l:r])
                    l_val = x_dots[l:r][0][0]
                    r_val = x_dots[l:r][-1][0]
                    
                    u_val = y_dots[u:t][0][1]
                    t_val = y_dots[u:t][-1][1]
                    #print((r-l)*(t-u))
                    if ans > (r_val-l_val)*(t_val-u_val):
                        ans = (r_val-l_val)*(t_val-u_val)
print(ans)


#y_dots = sorted(y_dots, key=lambda x: x[1])
#ans = INT_MAX