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 sys
import itertools

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

N, K = lr()
XY = [lr() for _ in range(N)]
XY.sort()
answer = float('inf')
# 端の4点、まずはx軸の2点を選ぶ
for left,right in itertools.combinations(range(N),2):
  width = XY[right][0] - XY[left][0]
  pts = sorted(XY[left:right+1], key = lambda xy: xy[1])
  if len(pts) < K:
    continue
  for D in range(len(pts) - K + 1):
    y_max = pts[D+K-1][1]
    y_min = pts[D][1]
    area = (y_max - y_min) * width
    if area < answer:
      answer = area
    
print(answer)