Raise a Fraction to a Real Power

Interpret numerator / denominator as a positive rational number, then raise it to power. This task returns a real number rather than an exact fraction; it covers the real-exponent part of the Rational Numbers reference.

Implement rational_to_real_power(numerator, denominator, power).

Input

numerator: The positive numerator.

denominator: The positive denominator.

power: The real-valued exponent.

Output

Return (numerator / denominator) raised to power.

Constraints

1 ≤ numerator, denominator ≤ 100. −6 ≤ power ≤ 6, with at most two decimal places. Answers are accepted within absolute or relative error 0.000001.

Examples

Input:
power = 0.5
numerator = 9
denominator = 4

Expected output:
expected = 1.5

Input:
double power = 0.5;
long long numerator = 9;
long long denominator = 4;

Expected output:
double expected = 1.5;

Input:
double power = 0.5;
long numerator = 9;
long denominator = 4;

Expected output:
double expected = 1.5;

Input:
power = -1.0
numerator = 2
denominator = 5

Expected output:
expected = 2.5

Input:
double power = -1.0;
long long numerator = 2;
long long denominator = 5;

Expected output:
double expected = 2.5;

Input:
double power = -1.0;
long numerator = 2;
long denominator = 5;

Expected output:
double expected = 2.5;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Rational Numbers