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:
import itertools
n, k = map(int, input().split())
p = []

vy = set()
vx = set()
for i in range(n):
    x, y = map(int, input().split())
    p.append((y,x))
    vy.add(y)
    vx.add(x)
vy = sorted(list(vy))
vx = sorted(list(vx))

min_area = float('inf')


for y in itertools.combinations(vy, r=2):
    for x in itertools.combinations(vx, r=2):
        cnt = 0
        for i in range(n):
            if y[0] <= p[i][0] <= y[1] and x[0] <= p[i][1] <= x[1]:
                cnt += 1
        if cnt >= k:
            min_area = min(min_area, (y[1]-y[0]) * (x[1]-x[0]))
print(min_area)