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 itertools

N,K = map(int, input().split())

XY = [[int(x) for x in input().split()] for _ in range(N)]
XY.sort()
X,Y = zip(*XY)

min_area = 5*10**18

for left,right in itertools.combinations(range(N),2):
  width = X[right] - X[left]
  pts = sorted(XY[left:right+1], key = lambda xy: xy[1])
  for D in range(len(pts)):
    if D + K - 1 >= len(pts):
      break
    y_max = pts[D+K-1][1]
    y_min = pts[D][1]
    area = (y_max - y_min) * width
    if area < min_area:
      min_area = area
    
print(min_area)