Let N be an n-bit positive integer, and let a, b, c, and k be positive integers less than N. Assume that the multiplicative inverse (mod N) of a is a^(k-1).

Give an O(n^3) algorithm for computing a^(b^c) mod N (i. e., a raised to the power bc with the result taken mod N). Any solution that requires computing bc is so inefficient that it will receive no credit. Hint: You can do this with a few application of algorithm.