Problem: 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.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999


Output

3999999996000000001

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline
import itertools
n,k=map(int,input().split())
X,Y,XY=[0]*n,[0]*n,[0]*n
for i in range(n):
  x,y=map(int,input().split())
  X[i],Y[i],XY[i]=x,y,[x,y]
X.sort()
Y.sort()
def count(x1,x2,y1,y2):
  ct=0
  for x,y in XY:
    if x1<=x<=x2 and y1<=y<=y2:
      ct+=1
  return ct
ans=float("inf")
for x1,x2 in itertools.combinations(X,2):
  for y1,y2 in itertools.combinations(Y,2):
    if count(x1,x2,y1,y2)==k:
      ans=min(ans,abs((x1-x2)*(y1-y2)))
print(ans)