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)]
X, Y = zip(*XY)
X_s = sorted(X)
Y_s = sorted(Y)

r = 10**20
for xi0 in range(N):
  for xi1 in range(xi0, N):
    for yi0 in range(N):
      for yi1 in range(yi0, N):
        x0 = X_s[xi0]
        x1 = X_s[xi1]
        y0 = Y_s[yi0]
        y1 = Y_s[yi1]
        c = 0
        for x, y in XY:
          if x0 <= x <=x1 and y0 <= y <= y1:
            c += 1
        if c >= K:
          r = min(r, (x1 - x0) * (y1 - y0))
print(r)