Superincreasing

An array $A$ of length $N$ containing **positive** integers is said to be *superincreasing* if each element is **strictly greater** than the sum of all the previous elements. That is, for each $i$ from $2$ to $N$, the condition $$ A_i \gt A_1 + A_2 + \ldots + A_{i-1} $$ should hold. For example, $A = [3, 5, 10, 42]$ is a superincreasing array, while $A = [1, 2, 3]$ is not ($3 = 1+2$, but it sho