Exact Fraction Arithmetic

Represent a fraction as [numerator, denominator]. Apply operation to first and second: add, subtract, multiply, or divide. For absolute, use only first. For power, raise first to the integer exponent and ignore second. Return lowest terms with a positive denominator. Normalize zero to [0, 1]. All divisions and negative powers in valid inputs are defined.

Implement rational_arithmetic(operation, first, second, exponent).

Input

operation: The operation name.

first: Two integers representing the first fraction.

second: Two integers representing the second fraction; use [0, 1] when unused.

exponent: The exponent for power; use 0 for other operations.

Output

Return [numerator, denominator] in reduced form with a positive denominator.

Constraints

operation is add, subtract, multiply, divide, absolute, or power. Both fraction components have magnitude at most 100; denominators are nonzero. −6 ≤ exponent ≤ 6. For divide, second has nonzero numerator. For a negative power, first has nonzero numerator. The 0th power is [1, 1], including 0⁰ by this task’s convention. Values fit signed 64-bit.

Examples

Input:
first = [1, 6]
second = [1, 4]
exponent = 0
operation = "add"

Expected output:
expected = [5, 12]

Input:
std::vector<long long> first = {1, 6};
std::vector<long long> second = {1, 4};
long long exponent = 0;
std::string operation = "add";

Expected output:
std::vector<long long> expected = {5, 12};

Input:
long[] first = new long[] {1, 6};
long[] second = new long[] {1, 4};
long exponent = 0;
string operation = "add";

Expected output:
long[] expected = new long[] {5, 12};

Input:
first = [2, 3]
second = [0, 1]
exponent = -2
operation = "power"

Expected output:
expected = [9, 4]

Input:
std::vector<long long> first = {2, 3};
std::vector<long long> second = {0, 1};
long long exponent = -2;
std::string operation = "power";

Expected output:
std::vector<long long> expected = {9, 4};

Input:
long[] first = new long[] {2, 3};
long[] second = new long[] {0, 1};
long exponent = -2;
string operation = "power";

Expected output:
long[] expected = new long[] {9, 4};

References

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

• Rational Numbers