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 itertools
N, K = [int(_) for _ in input().split()]
XY = [[int(_) for _ in input().split()] for _ in range(N)]
X, Y = [x for x, y in XY], [y for x, y in XY]
X_s, Y_s = sorted(X), sorted(Y)
ans = float('inf')
for x1, x2 in itertools.combinations(X_s, 2):
    for y1, y2 in itertools.combinations(Y_s, 2):
        k = sum([x1 <= X[i] <= x2 and y1 <= Y[i] <= y2 for i in range(N)])
        if k >= K:
            ans = min(ans, (x2 - x1) * (y2 - y1))
print(ans)