Heating

Description:

Input:

The first line contains single integer $$$n$$$ ($$$1 \le n \le 1000$$$) — the number of rooms.

Each of the next $$$n$$$ lines contains the description of some room. The $$$i$$$-th line contains two integers $$$c_i$$$ and $$$sum_i$$$ ($$$1 \le c_i, sum_i \le 10^4$$$) — the maximum number of radiators and the minimum total number of sections in the $$$i$$$-th room, respectively.

Output:

For each room print one integer — the minimum possible cost to install at most $$$c_i$$$ radiators with total number of sections not less than $$$sum_i$$$.

Sample Input:

4
1 10000
10000 1
2 6
4 6

Sample Output:

100000000
1
18
10

Note:

In the first room, you can install only one radiator, so it's optimal to use the radiator with $$$sum_1$$$ sections. The cost of the radiator is equal to $$$(10^4)^2 = 10^8$$$.

In the second room, you can install up to $$$10^4$$$ radiators, but since you need only one section in total, it's optimal to buy one radiator with one section.

In the third room, there $$$7$$$ variants to install radiators: $$$[6, 0]$$$, $$$[5, 1]$$$, $$$[4, 2]$$$, $$$[3, 3]$$$, $$$[2, 4]$$$, $$$[1, 5]$$$, $$$[0, 6]$$$. The optimal variant is $$$[3, 3]$$$ and it costs $$$3^2+ 3^2 = 18$$$.