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:
N,K=[int(x) for x in input().split()]
A=[]
X=[]
Y=[]
for i in range(N):
  x,y=[int(x) for x in input().split()]
  A.append([x,y])
  X.append(x)
  Y.append(y)

X.sort()
Y.sort()
ans=(X[-1]-X[0])*(Y[-1]-Y[0])

for i in range(N):
  for j in range(i+1,N):
    for k in range(N):
      for l in range(k+1,N):
        x1=X[i]
        x2=X[j]
        y1=Y[k]
        y2=Y[l]
        count=0
        for a in range(N):
          if x1<=A[a][0] and A[a][0]<=x2:
            if y1<=A[a][1] and A[a][1]<=y2:
              count+=1
        if count>=K:
          ans=min(ans, (y2-y1)*(x2-x1))
print(ans)