Food Resources

$M$ people are going on an adventure, and need to decide how to divide their food resources. There are $N$ types of food items with them, the $i$-th food type having $A_i$ units. A single person needs to eat one unit of food in one day. Each person must eat a single type of food for the entire duration of the adventure. Different people may eat the same, or different types of food. The duratio