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 = [[0, 0, 0] for _ in range(N)]
for i in range(N):
  x, y = map(int, input().split())
  XY[i] = [x, y, i]
X = sorted(XY)
Y = sorted(XY, key=lambda x: x[1])
rect = (X[-1][0] - X[0][0]) * (Y[-1][1] - Y[0][1])
for l in range(N - K + 1):
  for r in range(l + K - 1, N):
    for d in range(N - K + 1):
      for u in range(d + K - 1, N):
        if len([x for x in XY if X[l][0] <= x[0] <= X[r][0] and Y[d][1] <= x[1] <= Y[u][1]]) >= K:
          rect = min((X[r][0] - X[l][0]) * (Y[u][1] - Y[d][1]), rect)
print(rect)