B. XY Sequence
greedy
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 \([0, -3, -6, 1, -2]\).