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())
x=[0]*n;y=[0]*n
for i in range(n):x[i],y[i]=map(int,input().split())

ans=1e20
for i in range(n):
    for j in range(i+1, n):
        for a in range(n):
            for b in range(a+1, n):
                cnt=0
                x1=min(x[i],x[j])
                x2=max(x[i],x[j])
                y1=min(y[a],y[b])
                y2=max(y[a],y[b])
                for c in range(n):
                    if x1<=x[c]<=x2 and y1<=y[c]<=y2: cnt+=1
                if cnt>=k:
                    ans=min(ans,(x2-x1)*(y2-y1))
print(ans)