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:
n, k = map(int, input().split())
pos = []
for i in range(n):
    x, y = map(int, input().split())
    pos.append((x, y))

pos.sort()
minSq = 4000000000000000000

for l in range(n):
    lx, ly = pos[l]
    que = []
    for r in range(l, n):
        rx, ry = pos[r]
        que.append(ry)
        sizes = sorted(que)
        n_sizes = len(que)
        if n_sizes < k:
            continue
        for i_top in range(k - 1, n_sizes):
            top = sizes[i_top]
            bottom = sizes[i_top - k + 1]
            minSq = min(minSq, (top - bottom) * (rx - lx))

print(minSq)