Rikka with Graph

Problem Description

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them: For an undirected graph $G$ with $n$ nodes and $m$ edges, we can define the distance between $(i,j)$ ($\text{dist}(i,j)$) as the length of the shortest path between $i$ and $j$. The length of a path is equal to the number of the edges on it. Specially, if there are no path between $i$ and $j$, we make $\text{dist}(i,j)$ equal to $n$. Then, we can define the weight of the graph $G$ ($w_G$) as $\sum_{i=1}^n \sum_{j=1}^n \text{dist}(i,j)$. Now, Yuta has $n$ nodes, and he wants to choose no more than $m$ pairs of nodes $(i,j)(i \neq j)$ and then link edges between each pair. In this way, he can get an undirected graph $G$ with $n$ nodes and no more than $m$ edges. Yuta wants to know the minimal value of $w_G$. It is too difficult for Rikka. Can you help her?
In the sample, Yuta can choose $(1,2),(1,4),(2,4),(2,3),(3,4)$.

Input

The first line contains a number $t(1 \leq t \leq 10)$, the number of the testcases. For each testcase, the first line contains two numbers $n,m(1 \leq n \leq 10^6,1 \leq m \leq 10^{12})$.

Output

For each testcase, print a single line with a single number -- the answer.

Sample Input

1

4 5

Sample Output

14

Source

2017 Multi-University Training Contest - Team 5

https://acm.hdu.edu.cn/showproblem.php?pid=6090