Doubt in UVa problem 113 - Power of Cryptography

I saw this problem - 113- Power of cryptography on UVa OJ : [][1]

This does seem like a number theory or binary search question, but this AC solution is found on many blogs online - [][2]

This solution is pretty naive but still manages to pass. From what I knew, double in c++ supports only 15 significant digits. That means this solution should not have passed (p, of which nth root is to be found, has 200ish digits.)

Are test-cases of this question weak or this solution should have actually passed?

Also, share approaches apart from binary search to solve this question.

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15 significant digits is much more than 9 significant digits required in answer.

I think the test cases are weak!

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