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:
#https://atcoder.jp/contests/abc075/submissions/2242350
N,K=map(int,input().split())

points=[tuple(map(int,input().split())) for i in range(N)]
answer=10**19
sortx=sorted(points)
numberx = list(enumerate(sortx))

#n-k+1以降を左の頂点とすると点の数が明らかに足りない
for left,(x1,y1) in numberx[:N-K+1]:
  #left+K-1以降を右の頂点にしないと間に足りる点の数が入ってない
  for right,(x2,y2) in numberx[left+K-1:]:
    dx=x2-x1
    #left-rightの間でyについてsort
    sorty=sorted(y for x,y in sortx[left:right+1])
    #K個点を入れた状態で面積を求める
    for y3,y4 in zip(sorty,sorty[K-1:]):
      if y3<=y1 and y3<=y2 and y4>=y1 and y4>=y2:
        answer=min(answer,dx*(y4-y3))
         
print(answer)