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,Y=map(list,zip(*[list(map(int,input().split())) for i in range(N)]))
x=sorted(X)
y=sorted(Y)
c=[[0]*(N+1) for i in range(N+1)]
for i in range(N):
    c[x.index(X[i])+1][y.index(Y[i])+1]=1
for i in range(N):
    for j in range(N):
        c[i+1][j+1]+=c[i][j+1]+c[i+1][j]-c[i][j]
ans=5*10**18
for t in range(1,N):
    for b in range(t+1,N+1):
        for l in range(1,N):
            for r in range(l+1,N+1):
                count=c[b][r]-c[b][l-1]-c[t-1][r]+c[t-1][l-1]
                if count>=K:
                    ans=min(ans,(y[r-1]-y[l-1])*(x[b-1]-x[t-1]))
                    break
print(ans)