A14887. XY Sequence

You are given four integers $n$ , $B$ , $x$ and $y$ . You should build a sequence $a_0, a_1, a_2, \dots, a_n$ where $a_0 = 0$ and for each $i \ge 1$ you can choose:

- either $a_i = a_{i - 1} + x$
- or $a_i = a_{i - 1} - y$ .

Your goal is to build such a sequence $a$ that $a_i \le B$ for all $i$ and $\sum\limits_{i=0}^{n}{a_i}$ is maximum possible.

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. Next $t$ cases follow.

The first and only line of each test case contains four integers $n$ , $B$ , $x$ and $y$ ( $1 \le n \le 2 \cdot 10^5$ ; $1 \le B, x, y \le 10^9$ ).

It's guaranteed that the total sum of $n$ doesn't exceed $2 \cdot 10^5$ .

For each test case, print one integer — the maximum possible $\sum\limits_{i=0}^{n}{a_i}$ .

In the first test case, the optimal sequence $a$ is $[0, 1, 2, 3, 4, 5]$ .

In the second test case, the optimal sequence $a$ is $[0, 10^9, 0, 10^9, 0, 10^9, 0, 10^9]$ .

In the third test case, the optimal sequence $a$ is $[0, -3, -6, 1, -2]$ .