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 as cc
l = []
n,k = map(int, input().split())
xs,ys = set(),set()
t = 10**24
for _ in range(n):
  x,y = map(int, input().split())
  xs.add(x)
  ys.add(y)
  l.append((x,y))
xs = sorted(list(xs))
ys = sorted(list(ys))
for xl,xr in cc(xs,2):
  for yl,yr in cc(ys,2):
    cnt = 0
    for x,y in l:
      if xl<=x<=xr and yl<=y<=yr:
        cnt += 1
      if cnt >= k:
        s = (xr-xl)*(yr-yl)
        if t > s:
          t = s
print(t)