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:
import itertools

N,K = map(int, input().split())

X = []
Y = []

for _ in range(N):
  x,y = map(int, input().split())
  X.append(x)
  Y.append(y)

# 全部数えても間に合う

min_area = 5*10**18

for x1,x2 in itertools.combinations(X,2):
  for y1,y2 in itertools.combinations(Y,2):
    if x1 > x2:
      x1,x2 = x2,x1
    if y1 > y2:
      y1,y2 = y2,y1

    area = (x2-x1) * (y2-y1)
    if area > min_area:
      continue
      
    cnt = 0
    for x,y in zip(X,Y):
      if x1 <= x <= x2 and y1 <= y <= y2:
        cnt += 1
    if cnt < K:
      continue
      
    min_area = area
    
print(min_area)