Problem Statement

There are $N$ points on a two-dimensional coordinate plane. The coordinates of the $i$-th point are $(x_i, y_i)$.
For real numbers $a_1, a_2$, define
$f(x) = a_1 x + H$, which satisfies $f(0) = H$, and
$g(x) = a_2 x$, which satisfies $g(0) = 0$.
Find the minimum value of the following function $L(a_1, a_2)$.

$ L(a_1, a_2) = \displaystyle \sum_{i=1}^N \ \min \left\{ \left( y_i - f(x_i) \right)^2, \left( y_i - g(x_i) \right)^2 \right\} $


In other words, find the minimum value of the sum of the $2$nd powers of the lengths of the arrows in the figure above.

Input

$N$
$H$
$x_1\ y_1$
$x_2\ y_2$
$x_3\ y_3$
$\vdots$
$x_N\ y_N$

• All inputs are integers.
• $1 \leq N \leq 2 \times 10^3$
• $1 \leq H \leq 5 \times 10^2$
• $1 \leq x_i \leq 5 \times 10^2$
• $1 \leq y_i \leq 5 \times 10^2$

Output

Output the minimum value of $L$. Your answer is considered correct if its absolute or relative error from the expected solution is at most $10^{-5}$. The expected solution is guaranteed to have an absolute or relative error of at most $10^{-9}$ from the true value.

Sample

4
10
4 1
4 3
4 7
4 9

4

1
2
1 1

0

9
58
5 48
51 24
35 41
49 29
52 2
43 10
6 31
11 53
35 33

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