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=map(int,input().split())
P=[list(map(int,input().split())) for _ in range(n)]
X=sorted(list(map(lambda x:x[0],P)))
Y=sorted(list(map(lambda x:x[1],P)))
s=(X[0]-X[-1])*(Y[0]-Y[-1])
ans=0
for r in range(n-1,0,-1):
  for l in range(r):
    for u in range(n-1,0,-1):
      for b in range(u):
        c=0
        for p in P:
          if X[l]<=p[0]<=X[r] and Y[b]<=p[1]<=Y[u]:
            c+=1
        if c>=k:
          s=min(s,(X[r]-X[l])*(Y[u]-Y[b]))
        else:break
    if u==n-1 and b==0 and c<k:
      break
print(s)