Real Root of Quadratic Equation

Given three integers (a), (b), and (c) with (a \neq 0), consider the quadratic equation [ a x^2 + b x + c = 0, ]

Your task is to determine whether the equation has real solutions or not. If it does, output the larger root (possibly repeated) in the following format:

1. When outputting a rational number (v), it must be represented in its unique reduced form as follows. There exist unique integers (p) and (q) with (q > 0) and (\gcd(p,q)=1) such that (v=\frac{p}{q}). If (q=1) then output just the integer value, i.e. simply output (p); otherwise, output it as (p/q).

   For example:

   • If \(v = -0.5\), then \(p=-1\) and \(q=2\) so you should output -1/2.
   • If \(v = 0\), then \(p=0\) and \(q=1\) so you should output 0.

2. For solving the quadratic equation, consider the discriminant (\Delta = b^2 - 4ac):

   1. If \(\Delta < 0\), the equation has no real solutions; output NO.
   2. If \(\Delta \ge 0\), let \(x\) be the larger of the two solutions. Then:
      1. If \(x\) is rational, output it in the rational format described above.
      2. If \(x\) is irrational, it can be uniquely represented as \[

      x = q_1 + q_2 \sqrt{r}, ] where:

      • (q_1) and (q_2) are rational numbers with (q_2 > 0);
      • (r) is a positive integer greater than 1 and is square-free (i.e. there is no integer (d>1) such that (d^2 \mid r)).
      Output the answer as follows:
      1. If (q_1 \neq 0), first output (q_1) (in the rational format) followed by a plus sign +;
      2. Then, for the (\sqrt{r})-part, do the following:
         1. If (q_2 = 1), output sqrt({r});
         2. If (q_2) is an integer (and not 1), output {q2}*sqrt({r});
         3. If the reciprocal (q_3 = 1/q_2) is an integer, output sqrt({r})/{q3};
         4. Otherwise, if (q_2 = c/d) in lowest terms (with (c, d > 1) and (\gcd(c,d)=1)), output {c}*sqrt({r})/{d}.

   </p>

   In summary, if the quadratic equation has a real solution, output the larger one in the correct format as illustrated above; otherwise, output NO.

   inputFormat

   The input consists of three space-separated integers (a), (b), and (c) (with (a \neq 0)).

   outputFormat

   Output the larger real root in the required format if it exists; otherwise, output NO.

   sample

   1 -3 2

   2