Boxes

You have N pouches, each containing some number of marbles. The number of marbles contained in the ith box is denoted by ai. You need to put these pouches in at most M boxes. You can only choose consecutive pouches to put in a box. For each box, calculate the gcd of the number of marbles in each pouch in the box. Our goal is to find such a distribution of the pouches which maximizes the minimum gc