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:
N, K = map(int, input().split())
p = [list(map(int, input().split())) for i in range(N)]
t, b, l, r = 0, 0, 0, 0
area = []


for i in range(N):
  t = p[i][1]
  p1 = [a for a in p if a[1] <= t]
#  print(t, p1)
  for j in range(len(p1)):
    b = p1[j][1]
    p2 = [a for a in p1 if a[1] >= b]
#    print(b, p2)
    for k in range(len(p2)):
      r = p2[k][0]
      p3 = [a for a in p2 if a[0] <= r]
#      print(r, p3)
      for m in range(len(p3)):
        l = p3[m][0]
        p4 = [a for a in p3 if a[0] >= l]
#        print(l, p4)   
        if len(p4) >= K:
          tmp = (l-r)*(t-b)
          area.append(abs(tmp))
print(min(area))