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 = list(map(int,input().split()))

X = []
Y = []
Z = []
for i in range(N):
    x,y = list(map(int,input().split()))
    X.append(x)
    Y.append(y)
    Z.append([x,y])

X.sort()
Y.sort()

min_rec=10**27

for i in range(N-1):
    for j in range(i+1,N):
        for k in range(N-1):
            for l in range(k+1,N):
                count=0
                for n in range(N):
                    if Z[n][0]>=X[i] and Z[n][0]<=X[j] and Z[n][1]>=Y[k] and Z[n][1]<=Y[l]:
                        count+=1
                if count==K:
                    min_rec = min(min_rec,(X[j]-X[i])*(Y[l]-Y[k]))

print(min_rec)