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 bisect
from operator import itemgetter
N, K = map(int, input().split())
XY = [list(map(int, input().split())) for _ in range(N)]

XY.sort(key=itemgetter(0))
x, y = list(zip(*XY))

ans = 10**19
for l in range(N):
    for r in range(l, N):
        n = bisect.bisect_right(x, x[r]) - bisect.bisect_left(x, x[l])
        if n >= K:
            dx = x[r]-x[l]
            tmp = sorted(y[l:r+1])
            for i in range(n-K+1):
                dy = tmp[i+K-1] - tmp[i]
                ans = min(ans, dx*dy)
print(ans)