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mod to 10^9 + 7 for the modulo operation.modularExponentiation that takes a base a, an exponent b, and a modulo m, and computes a^b mod m using the square-and-multiply algorithm.monkeyMove function, call modularExponentiation with 2 as the base, n as the exponent, and mod as the modulo.2 from the result of the exponentiation to account for the two collision-free scenarios.mod to ensure a positive result.mod.