Implement 64-bit modular exponentiation safely

Q: Implement 64-bit modular exponentiation safely

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Question

Implement a function to compute (a^b) mod m where 0 ≤ a,b < 2^61−1 and 1 ≤ m < 2^61−1 using only 64-bit operations without overflow. Provide implementations for fast modular multiplication that avoids overflow and fast modular exponentiation. Include comprehensive tests and analyze the time and space complexity.

Implement 64-bit modular exponentiation safely

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