Let x1, x2, …, xn be a sequence of integers such that
(i) \minus{}1 \le x_i \le 2, for i \equal{} 1,2,3,\dots,n;
(ii) x_1 \plus{} x_2 \plus{} \cdots \plus{} x_n \equal{} 19; and
(iii) x_1^2 \plus{} x_2^2 \plus{} \cdots \plus{} x_n^2 \equal{} 99.
Let m and M be the minimal and maximal possible values of x_1^3 \plus{} x_2^3 \plus{} \cdots \plus{} x_n^3, respectively. Then \frac{M}{m} \equal{}
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>4<spanclass=′latex−bold′>(C)</span>5<spanclass=′latex−bold′>(D)</span>6<spanclass=′latex−bold′>(E)</span>7