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())
XY = [tuple(map(int, input().split())) for _ in range(N)]

Xs = set()
Ys = set()
for x,y in XY:
    Xs.add(x)
    Ys.add(y)


Xs = list(Xs)
Xs.sort()

Ys = list(Ys)
Ys.sort()

LX = len(Xs)
LY = len(Ys)
ans = 10**20

for i in range(LX):
    for j in range(i+1, LX):
        for k in range(LY):
            for l in range(k+1, LY):
                cnt = 0
                for x,y in XY:
                    if Xs[i] <= x <= Xs[j] and Ys[k] <= y <= Ys[l]:
                        cnt += 1

                if cnt >= K:
                    ans = min(ans, (Xs[j] - Xs[i])*(Ys[l] - Ys[k]))


print(ans)