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 PYTHON):

Solution:
import sys

N,K=map(int, sys.stdin.readline().split())
X=[]
Y=[]
XY=[]

for _ in range(N):
	x,y=map(int, sys.stdin.readline().split())
	X.append(x)
	Y.append(y)
	XY.append( (x,y) )

ans=float("inf")
for x1 in X:
	for y1 in Y:
		for x2 in X:
			for y2 in Y:
				if x1<x2 and y1<y2:
					cnt=0
					for x, y in XY:
						if x1<=x<=x2 and y1<=y<=y2:
							cnt+=1
	
					menseki=abs(x1-x2)*abs(y1-y2)
					if K<=cnt:
						ans=min(ans, menseki)
			
print ans