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:
from itertools import product
from operator import itemgetter
N, K = map(int, input().split())
XY = []
X, Y = [], []
for _ in range(N):
    x, y = map(int, input().split())
    X.append(x)
    Y.append(y)
    XY.append([x, y])
X.sort()
Y.sort()
XY.sort(key=itemgetter(1))

ans = 10 ** 19
for l, r, t in product(X, X, Y):
    if l > r:
        continue
    cnt = -K
    for x, y in XY:
        if y < t:
            continue
        if l <= x <= r:
            cnt += 1
            if cnt >= 0:
                area = (r - l) * (y - t)
                if area < ans:
                    ans = area
                break

print(ans)