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:
# -*- coding: utf-8 -*-
N, K = map(int, input().split(' '))
points = [list(map(int, input().split(' '))) for i in range(N)]

X = list(set([x for x, y in points]))
Y = list(set([y for x, y in points]))

X.sort()
Y.sort()

ans = float('inf')
for i, min_x in enumerate(X):
    for max_x in X[i+1:]:
        for j, min_y in enumerate(Y):
            for max_y in Y[j + 1:]:
                m = (max_x - min_x) * (max_y - min_y)
                internal_points = [(x, y) for x, y in points if min_x <= x <= max_x and min_y <= y <= max_y]
                if len(internal_points) >= K:
                    ans = min(ans, m)

print(ans)