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:
def solve():
  n, k = map(int, input().split())
  p = [tuple(map(int, input().split())) for i in range(n)]
  p.sort()
  ans = 4000000000000000000
  for i in range(k, n + 1):
      for j in range(n - i + 1):
          x = p[i + j - 1][0] - p[j][0]
          s = [p[a][1] for a in range(j, i + j)]
          s.sort()
          y = 4000000000
          for a in range(i - k + 1):
            y = min(y, s[a + k - 1] - s[a])
          ans = min(ans, x * y)
  print(ans)
solve()