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())
XY = [list(map(int, input().split())) for _ in range(N)]
XY.sort()
r = 10**20
for xi0 in range(N - K + 1):
  for xi1 in range(K + xi0 - 1, N):
    x = XY[xi1][0] - XY[xi0][0]
    XY_ys = sorted(XY[xi0:xi1 + 1], key=lambda a: a[1])
    for yi0 in range(len(XY_ys) - K + 1):
      y = XY_ys[yi0 + K - 1][1] - XY_ys[yi0][1]
      r = min(r, x * y)
print(r)