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())
p_list = [[0] * 2 for i in range(N)]
for i in range(N):
    x, y = map(int, input().split())
    p_list[i] = [x, y]

p_list.sort()
ans = float('inf')
for i in range(N - K + 1):
    for j in range(i + K - 1, N):
        x = abs(p_list[j][0] - p_list[i][0])
        y_list = []
        for k in range(i, j + 1):
            y_list.append((p_list[k][1]))
        y_list.sort()
        for k in range(len(y_list) - K + 1):
            ans = min(ans, x * abs(y_list[k + K - 1] - y_list[k]))

print(ans)