Planting Roses

There are $N$ different colors of roses. You have $A_i$ roses of the $i$-th color. Your garden has $M$ pots arranged in a line, numbered $1$ to $M$. In each pot, you can either plant one rose or leave it empty. In the interest of aesthetics, you would like to follow these two rules: 1. Two adjacent pots cannot have differently colored roses. That is, there must not exist an integer $i$ such