The following algorithm takes as input two non-negative integers, x and y, and returns the product of x and y. fastmult(x, y) input: two non-negative integers, x and y output: the product of x and y if (y = 0), return( 0 ) z : = ⌊y/2⌋ p : = fastmult(x, z) // the recursive call if (y is even) return( 2 · p ) else return( 2 · p + x ) end-if use induction to prove that the algorithm returns the correct value.