13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6d8,

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}^{

XY Sequence

Examples