CF1301C.Ayoub's function

Ayoub thinks that he is a very smart person, so he created a function $f(s)$, where $s$ is a binary string (a string which contains only symbols "0" and "1"). The function $f(s)$ is equal to the number of substrings in the string $s$ that contains at least one symbol, that is equal to "1".

More formally, $f(s)$ is equal to the number of pairs of integers $(l, r)$, such that $1 \leq l \leq r \leq |s|$ (where $|s|$ is equal to the length of string $s$), such that at least one of the symbols $s_l, s_{l+1}, \ldots, s_r$ is equal to "1".

For example, if $s = $"01010" then $f(s) = 12$, because there are $12$ such pairs $(l, r)$: $(1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5)$.

Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers $n$ and $m$ and asked him this problem. For all binary strings $s$ of length $n$ which contains exactly $m$ symbols equal to "1", find the maximum value of $f(s)$.

Mahmoud couldn't solve the problem so he asked you for help. Can you help him?

Ayoub 认为自己非常聪明，因此他定义了一个函数 $f(s)$，其中 $s$ 是一个二进制字符串（即仅由字符 "0" 和 "1" 组成的字符串）。函数 $f(s)$ 的值等于字符串 $s$ 中至少包含一个 "1" 的子串的个数。

更准确地说，$f(s)$ 等于满足如下条件的整数对 $(l, r)$ 的个数：$1 \leq l \leq r \leq |s|$（其中 $|s|$ 表示字符串 $s$ 的长度），且子串 $s_l, s_{l+1}, \ldots, s_r$ 中至少有一个字符为 "1"。

例如，若 $s = $"01010"$，则 $f(s) = 12$，因为满足条件的 $(l, r)$ 共有 $12$ 对：$(1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5)$。

Ayoub 还认为自己比 Mahmoud 更聪明，于是他给了 Mahmoud 两个整数 $n$ 和 $m$，并提出如下问题：在所有长度为 $n$、且恰好包含 $m$ 个 "1" 的二进制字符串 $s$ 中，求 $f(s)$ 的最大可能值。

Mahmoud 无法解决这个问题，于是向你求助。你能帮他吗？

The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^5$) — the number of test cases. The description of the test cases follows.

The only line for each test case contains two integers $n$, $m$ ($1 \leq n \leq 10^{9}$, $0 \leq m \leq n$) — the length of the string and the number of symbols equal to "1" in it.

输入包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 10^5$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例仅有一行，包含两个整数 $n$ 和 $m$（$1 \leq n \leq 10^{9}$，$0 \leq m \leq n$），分别表示字符串的长度以及其中字符 "1" 的个数。

For every test case print one integer number — the maximum value of $f(s)$ over all strings $s$ of length $n$, which has exactly $m$ symbols, equal to "1".

对于每个测试用例，输出一个整数——在所有长度为 $n$ 且恰好包含 $m$ 个字符 "1" 的字符串 $s$ 中，$f(s)$ 的最大值。

In the first test case, there exists only $3$ strings of length $3$, which has exactly $1$ symbol, equal to "1". These strings are: $s_1 = $"100", $s_2 = $"010", $s_3 = $"001". The values of $f$ for them are: $f(s_1) = 3, f(s_2) = 4, f(s_3) = 3$, so the maximum value is $4$ and the answer is $4$.

In the second test case, the string $s$ with the maximum value is "101".

In the third test case, the string $s$ with the maximum value is "111".

In the fourth test case, the only string $s$ of length $4$, which has exactly $0$ symbols, equal to "1" is "0000" and the value of $f$ for that string is $0$, so the answer is $0$.

In the fifth test case, the string $s$ with the maximum value is "01010" and it is described as an example in the problem statement.

在第一个测试用例中，仅存在 $3$ 个长度为 $3$、且恰好包含 $1$ 个字符 "1" 的字符串。这些字符串为：$s_1 = $"100", $s_2 = $"010", $s_3 = $"001"。它们对应的 $f$ 值分别为：$f(s_1) = 3, f(s_2) = 4, f(s_3) = 3$，因此最大值为 $4$，答案为 $4$。

在第二个测试用例中，使 $f$ 值最大的字符串 $s$ 是 "101"。

在第三个测试用例中，使 $f$ 值最大的字符串 $s$ 是 "111"。

在第四个测试用例中，唯一一个长度为 $4$、且恰好包含 $0$ 个字符 "1" 的字符串 $s$ 是 "0000"，该字符串对应的 $f$ 值为 $0$，因此答案为 $0$。

在第五个测试用例中，使 $f$ 值最大的字符串 $s$ 是 "01010"，该字符串已在题目描述中作为示例给出。