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Sad this behaviour is described but not tested, yes...
The fork handles the right associativity of the power operator.
The problem said "left-associativity of all operators but ^". So I think "^" has right-associativity.
For example, "2^3^4" will be interpreted into "23^4^" with your solution. But it should be "234^^" if "^" has right-associativity.