Complete the design of the following algorithm for performing integer multiplication in time . (This is slower than the standard algorithm, but its verification and analysis will test your abilities.) We use a technique similar to the standard divide-and-conquer algorithm. Instead of dividing the inputs and into two parts, we divide them into three parts. Suppose and have bits, where is a power of . Break into three parts each with bits. Break into three parts each with bits. Then,

t=ad = (a + b)(d+e) Ty :=be T4 = (a + c)(d+1) T's ef T = (b + c)(e+ 1:=7,24/3 + (r2 - 11 - )2 + (rs + re-r1 - )22n/3 + (rs -- 13 - rs)2"/3 +rs