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 _ in range(n)]
x=[t[0] for t in xy]
y=[t[1] for t in xy]

res=[]
for i in range(n-1):
    for j in range(i+1,n):
        for a in range(n-1):
            for b in range(a+1,n):
                l=min(x[i],x[j])
                r=max(x[i],x[j])
                d=min(y[a],y[b])
                u=max(y[a],y[b])
                tk=0
                for t in xy:
                    if l<=t[0]<=r and d<=t[1]<=u:
                        tk+=1
                if tk>=k:
                    res.append((r-l)*(u-d))
print(min(res))