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=[[int(x) for x in input().split()] for _ in range(N)]

xs=[x for x,_ in p]
ys=[y for _,y in p]
q=[(x,y) for x in xs for y in ys]

up=[set() for _ in range(len(q))]
dn=[set() for _ in range(len(q))]

for i in range(len(q)):
	xi,yi=q[i]
	for j in range(len(p)):
		xj,yj=p[j]
		if xj >= xi and yj >= yi:
			up[i].add(j)
		if xj <= xi and yj <= yi:
			dn[i].add(j)

ans=10**999

for i in range(len(q)):
	for j in range(len(q)):
		if len(up[i] & dn[j]) >= K:
			xi,yi=q[i]
			xj,yj=q[j]
			ans=min(ans, abs(xj-xi)*abs(yj-yi))

print(ans)