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 (7.3.0) (judge verdict: Accepted)

def check(x1,x2,y1,y2):
  p1=x1
  p2=x2
  q1=y1
  q2=y2
  if x1<=x2:
    x1=p1
    x2=p2
  else:
    x1=p2
    x2=p1
  if y1<=y2:
    y1=q1
    y2=q2
  else:
    y1=q2
    y2=q1
  count=0
  for ttx,tty in xy:
    if x1<=ttx<=x2 and y1<=tty<=y2:
      count+=1
  if count>=k:
    res=True
  else:
    res=False
  return res

n,k=map(int,input().split())
x,y=[],[]
xy=[]
for i in range(n):
  a,b=map(int,input().split())
  x.append(a)
  y.append(b)
  xy.append((a,b))
from itertools import combinations
ans=10**20
for xx in combinations(x,2):
  for yy in combinations(y,2):
    if check(xx[0],xx[1],yy[0],yy[1]):
      tmp=abs(xx[0]-xx[1])*abs(yy[0]-yy[1])
      ans=min(ans,tmp)
print(ans)