XY Sequence

2000ms

262144K

Description:

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.

Input:

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 $$$2 \cdot 10^5$$$.

Output:

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

Sample Input:

3
5 100 1 30
7 1000000000 1000000000 1000000000
4 1 7 3

Sample Output:

15
4000000000
-10

Note:

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 $$$[0, -3, -6, 1, -2]$$$.

Informação

Provedor Codeforces

Código CF1657B