Forming Groups

There are $n$ students, numbered from $1$ to $n$, who need to form groups for an upcoming hackathon. You are student $1$, the captain. Student $i$ has skill level $a_i$.

Students $2$ to $n$ stand in a line from left to right, in order. You can stand between any two students, to the left of student $2$, or to the right of student $n$. The order of the $n - 1$ students cannot change.

You can also choose the number of groups $k$, where $k > 1$ and $k$ is a divisor of $n$. The groups are numbered from $1$ to $k$. After you choose your position and $k$, the students are grouped as follows.

The first student from the left is assigned to group $1$, the second to group $2$, and so on up to the $k$-th student, who is assigned to group $k$. The $(k+1)$-th student is assigned to group $1$, the $(k+2)$-th to group $2$, and this pattern continues until the $n$-th student, who is assigned to group $k$.

Formally, for each $j$ ($1 \le j \le k$) and each $i$ ($0 \le i < n/k$), the $(i \times k + j)$-th student from the left is assigned to group $j$. Every student is in exactly one group, and all groups have the same number of students.

The skill level of a group is the sum of the skill levels of its students. Choose your position and $k$ to minimize the ratio $x_{\max}/x_{\min}$, where $x_{\max}$ is the largest group skill level and $x_{\min}$ is the smallest.