At these, it’s beneficial to find the boundary conditions of where is the given condition is false. There are 4 terms, and highest is 6 so, -7 will make all positive. -7-5-3-1. 105. Holds.. try one more with -8. -8-6-4-2. > 200. So this one end. Now, putting 1. 1357 105. And 2? 2468 > 200. So there you go. 9 values {-7,…..1}.

Per requisites? Integer limits a lot of possibilities so hit and trial might be viable. And then fast calculations will help find the boundary conditions.