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())
P= [list(map(int, input().split())) for i in range(N)]
P=sorted(P)
pi=list(enumerate(P))
minA=float("inf")
for il,xyl in pi[:N-1]:
    left=xyl[0]
    for ir,xyr in pi[il+1:]:
        right=xyr[0]
        insd=[xy_ for i,xy_ in pi if xyl[0]<=xy_[0]<=xyr[0]]
        insd=sorted(insd,key=lambda xx:xx[1])
        in_L=len(insd)
        if in_L<K:continue
        for jd in range(in_L-K+1):
            ju=jd+K-1
            down=insd[jd][1]
            upper=insd[ju][1]
            minA=min(minA,(upper-down)*(right-left))

print(minA)