Raise a Number to a Fractional Power

The exponent is numerator / denominator. Raise base_value to that exponent and return the real-valued result. For example, an exponent of 1/3 gives the positive cube root.

Implement real_to_rational_power(base_value, numerator, denominator).

Input

base_value: The positive base.

numerator: The exponent numerator.

denominator: The exponent denominator.

Output

Return base_value raised to numerator / denominator.

Constraints

0.1 ≤ base_value ≤ 100, with at most two decimal places. −6 ≤ numerator ≤ 6; 1 ≤ denominator ≤ 10. Answers are accepted within absolute or relative error 0.000001.

Examples

Input:
numerator = 1
base_value = 8.0
denominator = 3

Expected output:
expected = 2.0

Input:
long long numerator = 1;
double base_value = 8.0;
long long denominator = 3;

Expected output:
double expected = 2.0;

Input:
long numerator = 1;
double base_value = 8.0;
long denominator = 3;

Expected output:
double expected = 2.0;

Input:
numerator = -1
base_value = 16.0
denominator = 2

Expected output:
expected = 0.25

Input:
long long numerator = -1;
double base_value = 16.0;
long long denominator = 2;

Expected output:
double expected = 0.25;

Input:
long numerator = -1;
double base_value = 16.0;
long denominator = 2;

Expected output:
double expected = 0.25;

References

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

• Rational Numbers