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())
x,y=[[0,0] for i in range(n)],[[0,0] for i in range(n)]
xy=[list(map(int,input().split())) for i in range(n)]
for i in range(n):
    x_sub,y_sub=xy[i]
    x[i][0]=x_sub
    x[i][1]=i
    y[i][0]=y_sub
    y[i][1]=i
x.sort()
y.sort()
ans=(10**18)*5
for i1 in range(n):
    i1_sub=n-i1
    for l1 in range(i1_sub,1,-1):
        for i2 in range(n):
            i2_sub=n-i2
            for l2 in range(i2_sub,1,-1):
                x_sub1=x[i1][0]
                x_sub2=x[i1+l1-1][0]
                y_sub1=y[i2][0]
                y_sub2=y[i2+l2-1][0]
                z=[0]*n
                for i in range(n):
                    if x_sub1<=xy[i][0]<=x_sub2 and y_sub1<=xy[i][1]<=y_sub2:
                        if z[i]==0:
                            z[i]=1
                if sum(z)>=k:
                    ans=min((x_sub2-x_sub1)*(y_sub2-y_sub1),ans)
                else:
                    break
print(ans)