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 combinations

n, k = (int(x) for x in input().split())
XY = [tuple(int(x) for x in input().split()) for _ in range(n)]

ans = 10**20
X = []
Y = []
for x, y in XY:
    X.append(x)
    Y.append(y)

ans = 10**20
for ax, bx in combinations(X, 2):
    if ax > bx:
        ax, bx = bx, ax
    for ay, by in combinations(Y, 2):
        if ay > by:
            ay, by = by, ay
        count = 0
        for x, y in XY:
            if ax <= x <= bx and ay <= y <= by:
                count += 1
        if count >= k:
            ans = min(ans, (bx - ax) * (by - ay))

print(ans)