Magic Squares

You have $N$ magic squares (numbered from $1$ to $N$). For each magic square, you can set the length of its side to any non-negative integers. The cost of each magic square is proportional to its area; magic square $i$ has a cost of $C_i$ per unit area. In other words, if the length of magic square $i$ is set to $k$, then it will cost you $k^2 \cdot C_i$.

You want to build a wall with a length of $D$ using these magic squares. You have to line up all your magic squares next to each other, and their total length has to be exactly $D$. The base of each magic square must fully touch the floor, i.e. you are not allowed to rotate the magic squares.

Determine the minimum total cost to build the wall.

This problem has multiple test cases. The first line consists of an integer $T$ ($1 ≤ T ≤ 20$), which represents the number of test cases.

Each test case consists of two lines. The first line consists of two integers $N$ $D$ ($1 ≤ N ≤ 10\, 000$; $1 ≤ D ≤ 10^7$). The second line consists of $N$ integers $C_i$ ($1 ≤ C_i ≤ 10\, 000$).

For each test case, output an integer in a single line representing the minimum total cost to build the wall.