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())
xys = []
for i in range(N):
  x, y = map(int, input().split())
  xys.append((x, y))
xs = sorted(map(lambda xy: xy[0], xys))
ys = sorted(map(lambda xy: xy[1], xys))
rs = []
for i in range(N):
  for j in range(i+1, N):
    x1 = xs[i]
    x2 = xs[j]
    for k in range(N):
      for l in range(k+1, N):
        y1 = ys[k]
        y2 = ys[l]
        n = len([(x, y) for x, y in xys if x1 <= x <= x2 and y1 <= y <= y2])
        #xys2 = filter(lambda xy: x1 <= xy[0] <= x2 and y1 <= xy[1] <= y2, xys)
        if n >= K:
          r = (x2-x1)*(y2-y1)
          rs.append(r)
r = min(rs)
print(r)