Ayoub's Function

Problem Description

Define the function $f(s)$, where $s$ is a 01 string, as the number of substrings of $s$ that contain at least one 1.

You are given a string $s$ with length $n$ and exactly $m$ 1s. Find the maximum possible value of $f(s)$.

Input Format

The input consists of multiple test cases.

The first line contains an integer $T$ ($1 \le T \le 10^5$), the number of test cases.

Each of the next $T$ lines contains two integers $n, m$ ($1 \le n \le 10^9$, $0 \le m \le n$).

Output Format

Output $T$ lines, each containing one integer: the answer.

Sample Input

5
3 1
3 2
3 3
4 0
5 2

Sample Output

4
5
6
0
12

Sample Explanation

First test case: when $s = \texttt{010}$, $f(s) = 4$.

Second test case: when $s = \texttt{101}$, $f(s) = 5$.

Third test case: when $s = \texttt{111}$, $f(s) = 6$.

Fourth test case: when $s = \texttt{0000}$, $f(s) = 0$.

Fifth test case: when $s = \texttt{01010}$, $f(s) = 12$.