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: Accepted)

N,K=map(int,input().split())
X, Y, XY = [], [], []
for i in range(N):
  x, y = map(int,input().split())
  X += [x]
  Y += [y]
  XY += [[x,y]]
  
ans = 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):
        boxed = 0
        for i in range(N):
          if (X[x1] - X[i])*(X[x2]-X[i])<=0 and (Y[y1] - Y[i])*(Y[y2]-Y[i])<=0:
            boxed+= 1
        if boxed >= K: 
          ans = min(ans,abs(X[x1]-X[x2])*abs(Y[y1]-Y[y2]))
          #print(abs(X[x1]-X[x2])*abs(Y[y1]-Y[y2]))
print(ans)