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: Time Limit Exceeded)

n,k = map(int,input().split())
ary = [list(map(int,input().split())) for _ in range(n)]
ary_x = sorted(ary)
ary_y = sorted(ary,key=lambda x:(x[1],x[0]))
ans = float("Inf")

for xi in range(n):
    for xj in range(1,n):
        for yi in range(n):
            for yj in range(1,n):
                count = 0
                lx,rx = ary_x[xi][0],ary_x[xj][0]
                by,uy = ary_y[yi][1],ary_y[yj][1]

                for i in range(n):
                    if lx <= ary[i][0] <= rx and by <= ary[i][1] <= uy:
                        count += 1
                if count >= k:
                    ans = min(ans,(rx - lx) * (uy - by))
print(ans)