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=[list(map(int,input().split())) for i in range(n)]

def check(x1,y1,x2,y2):
    cnt=0
    for node in xy:
        x,y=node
        if x1<=x<=x2 and y1<=y<=y2:
            cnt+=1
    return cnt

xlis=[]
ylis=[]
for itm in xy:
    x,y=itm
    xlis.append(x)
    ylis.append(y)
xlis.sort()
ylis.sort()

ans=10**20
from itertools import *
for tmp1 in combinations(xlis,2):
    for tmp2 in combinations(ylis,2):
        x1,x2=tmp1
        y1,y2=tmp2
        ret = check(x1,y1,x2,y2)
        if ret==k:
            ans=min(ans,(x2-x1)*(y2-y1))

print(ans)