Let x be a string over some finite and fixed alphabet (think English alphabet).

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Let x be a string over some finite and fixed alphabet (think English alphabet). Given an integer k we use x^k to denote the string obtained by concatenating k copies of x. If x is the string HELLO then x^3 is the string HELLOHELLOHELLO. A repetition of x is a prefix of x^k for some integer k. Thus HELL and HELLOHELL are both repetitions of HELLO. An interleaving of two strings x and y is any string that is obtained by shuffling a repetition of x with a repetition of y. For example HELwoLOHELLrldwOH is an interleaving of HELLO and world. Describe an algorithm that takes three strings x, y, z as input and decides whether z is an interleaving of x and y. Designe effective algorithm for this task.