Problem Statement

The hero taiga is trying to defeat $1$ monster. taiga's clumsiness is $X$, and his mp is $10^{100}$. The monster's combat power is $A$. Before fighting the monster, taiga can use the following magic 0 or more times.

• Choose an integer $k$ satisfying $1 \le k \le A$, and replace $A$ with $A-k$. Then, consume $k^2+X$ mp.

When taiga fights the monster, he can defeat it only if $A=0$; otherwise, he fails to defeat it and loses. Find the minimum mp consumed when he uses magic appropriately before the fight and defeats the monster.

You are given $T$ test cases; find the answer for each of them.

Constraints

Input

$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$

Each test case is given in the following format.

$X$ $A$

Output

Output $T$ lines. On the $i$-th line, output the answer for $\mathrm{case}_i$.

Sample

3
3 3
6 29
100000 100000

11
145
63245648