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:
import sys
def MI(): return map(int,sys.stdin.readline().rstrip().split())

N,K = MI()
xy = [tuple(MI()) for i in range(N)]

xy.sort()

from operator import itemgetter

ans = 10**19
for i in range(N-1):
    for j in range(i+1,N):
        a = xy[j][0]-xy[i][0]
        A = xy[i:j+1]
        if len(A) >= K:
            A = sorted(A, key=itemgetter(1))
            b = 10**18
            for k in range(len(A)-K+1):
                b = min(b,A[k+K-1][1]-A[k][1])
            ans = min(ans,a*b)

print(ans)