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が小さい
#xi,yi全て試す

#for ループ変更
import itertools
n,k = map(int, input().split( ))

p = []
x = []
y = []
for i in range(n):
    xi,yi = map(int, input().split( ))
    p.append((xi,yi))
    x.append(xi)
    y.append(yi)

y = list(set(y))
x = list(set(x))
x.sort()
y.sort()
lx = len(x)
ly = len(y)
ans = 10**20
for xi,xj in itertools.combinations(x,2):
    for yi,yj in itertools.combinations(y,2):
        cnt = 0
        for xk,yk in p:
            if xi <= xk and xk<=xj and yi <=yk and yk<=yj:
                        cnt += 1
        if cnt >= k:
            ans = min(ans, (xj-xi)*(yj-yi))
print(ans)