G - 方程式 /

問題文

• 1\lt x \lt 2 の範囲に解をただ 1 つ持つ

1\lt x \lt 2 を満たす方程式の解を計算してください。

制約

• 1 \leq a \leq 10^9
• 1 \leq b \leq 10^9
• -10^9 \leq c \leq 10^9
• 入力は全て整数
• 与えられた方程式は、1\lt x \lt 2 の範囲に解をただ 1 つ持つ

入力

a b c


入力例 1

32 2 -246


出力例 1

1.500000000000000000


x = 1.5 のとき、ax^5+bx+c=32\times(1.5)^5 + 2\times1.5 - 246 = 0 を満たします。

入力例 2

12 3 -45


出力例 2

1.279562760087743278


Score : 6 points

Problem Statement

Assume that the equation a x^5 + bx + c=0 satisfies the condition below.

• It has exactly one solution in the interval 1\lt x \lt 2.

Find the solution of the equation in the interval 1\lt x \lt 2.

Constraints

• 1 \leq a \leq 10^9
• 1 \leq b \leq 10^9
• -10^9 \leq c \leq 10^9
• All values in input are integers.
• The given equation has exactly one solution in the interval 1\lt x \lt 2.

Input

Input is given from Standard Input in the following format:

a b c


Output

Print the answer. Your output will be judged as correct when its absolute or relative error from the judge's answer is at most 10^{-9}.

Sample Input 1

32 2 -246


Sample Output 1

1.500000000000000000


For x = 1.5, we have ax^5+bx+c=32\times(1.5)^5 + 2\times1.5 - 246 = 0.

Sample Input 2

12 3 -45


Sample Output 2

1.279562760087743278