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
N,K=map(int,input().split())

xs = set()
ys = set()
inl = []

for i in range(N):
    x,y=map(int,input().split())
    inl.append((x,y))
    xs.add(x)
    ys.add(y)

xs = list(xs)
ys = list(ys)
xs.sort()
ys.sort()

res = 9223372036854775807
for xlow, xhi in combinations(xs,2):
    for ylow, yhi in combinations(ys,2):
        cnt = 0
        for x, y in inl:
            cnt += (x >= xlow and x <= xhi and y >= ylow and y <= yhi)
        if cnt == K:
            res = min(res,(xhi - xlow) * (yhi - ylow))
print(res)