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:
from itertools import combinations

n, k = map(int, input().split())
xlist, ylist, xy = [], [], []
for _ in range(n):
  x, y = map(int, input().split())
  xlist.append(x)
  ylist.append(y)
  xy.append((x, y))

xlist.sort()
ylist.sort()
ans = (xlist[-1] - xlist[0]) * (ylist[-1] - ylist[0])
for x1, x2 in combinations(xlist, r=2):
  for y1, y2 in combinations(ylist, r=2):
    tmpk = 0
    for i in range(n):
      if x1 <= xy[i][0] <= x2 and y1 <= xy[i][1] <= y2:
        tmpk += 1

      if tmpk >= k:
        tmp_ans = (x2 - x1) * (y2 - y1)
        if ans > tmp_ans:
          ans = tmp_ans

print(ans)