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())
X = []; Y = []
xy = []
for i in range(N):
  x, y= map(int, input().split())
  xy.append((x, y))
  X.append(x); Y.append(y)

ans = 10**20
x2 = list(itertools.combinations(X, 2))
y2 = list(itertools.combinations(Y, 2))

for xi, xj in x2:
  if xj < xi:
    xi, xj = xj, xi
  for yi, yj in y2:
    if yj < yi:
      yi, yj = yj, yi
    n = 0
    for x, y in xy:
      if xi<=x<=xj and yi<=y<=yj:
        n += 1
    if n >= K:
      ans = min(ans, (xj-xi)*(yj-yi))

print(ans)