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 sys
from itertools import combinations
read = sys.stdin.read

N, K, *xy = map(int, read().split())
xy = sorted(zip(*[iter(xy)] * 2))
X, Y = zip(*xy)
answer = 10 ** 20

for left, right in combinations(range(N), 2):
    width = X[right] - X[left]
    tmp_Y = sorted(Y[left:right + 1])
    h = len(tmp_Y)
    for i in range(h):
        if i + K > h:
            break

        S = width * (tmp_Y[i + K - 1] - tmp_Y[i])
        if S < answer:
            answer = S

print(answer)