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, *L = map(int, open(0).read().split())
L = [(x,y) for x,y in zip(*[iter(L)]*2)]
ans = float('inf')
for m in combinations(L,2):
  for n in combinations(L,2):
    mx = min(m,key=lambda x:x[0])[0]
    Mx = max(m,key=lambda x:x[0])[0]
    my = min(n,key=lambda x:x[1])[1]
    My = max(n,key=lambda x:x[1])[1]
    cnt = 0
    for x,y in L:
      if mx<=x<=Mx and my<=y<=My:
        cnt += 1
    if cnt>=K:
      ans = min(ans, (Mx-mx)*(My-my))
print(ans)