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:
def i1():
 return int(input())
def i2():
 return [int(i) for i in input().split()]
[n,k]=i2()
x=[]
y=[]
zz=[]
for i in range(n):
 z=i2()
 x.append([z[0],i])
 y.append([z[1],i])
 zz.append(z)
x.sort()
y.sort()
xx=[i[1] for i in x]
yy=[i[1] for i in y]
a=float("inf")
for i in range(n):
 for j in range(i,n):
  for kk in range(n):
   for l in range(kk,n):
     if len(set(xx[i:j+1])&set(yy[kk:l+1]))==k:
         a=min(a,(zz[xx[j]][0]-zz[xx[i]][0])*(zz[yy[l]][1]-zz[yy[kk]][1]))
print(a)