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:
from itertools import combinations as comb
N, K = map(int, input().split())
ans = (2 * 10 ** 9) ** 2 + 1
choice = min(K, 4)
xs = [0] * N
ys = [0] * N
for i in range(N):
	xs[i], ys[i] = map(int, input().split())

for idxs in comb(range(N), choice):
	x_mx = y_mx = - 10 ** 9
	x_mn = y_mn = 10 ** 9
	for i in idxs:
		x_mx = max(x_mx, xs[i])
		y_mx = max(y_mx, ys[i])
		x_mn = min(x_mn, xs[i])
		y_mn = min(y_mn, ys[i])
	in_num = sum(x_mn <= xs[i] <= x_mx and y_mn <= ys[i] <= y_mx for i in range(N))
	area = (x_mx - x_mn) * (y_mx - y_mn)
	if in_num >= K and area < ans:
		ans = area
print(ans)