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 sys import stdin
def input():
    return stdin.readline().strip()

n, k = map(int, input().split())
xy  = []
for _ in range(n):
    i, j = map(int, input().split())
    xy.append((i, j))

xy.sort()

# decide left, right, down
ans = float('inf')
for left in range(n-k+1):
    for right in range(left+k-1, n):
        choose = sorted(xy[left:right+1], key=lambda x: x[1])
        for down in range(len(choose)-k+1):
            area = (xy[right][0] - xy[left][0]) * (choose[down+k-1][1] - choose[down][1])
            if area < ans:
                ans = area

print(ans)