| This is the easy version of the problem. In this version, $n=m$ and the time limit is lower. You can make hacks only if both versions of the problem are solved. | |
| In the court of the Blue King, Lelle and Flamm are having a performance match. The match consists of several rounds. In each round, either Lelle or Flamm wins. | |
| Let $W_L$ and $W_F$ denote the number of wins of Lelle and Flamm, respectively. The Blue King considers a match to be successful if and only if: | |
| * after every round, $\gcd(W_L,W_F)\le 1$; * at the end of the match, $W_L\le n, W_F\le m$. | |
| Note that $\gcd(0,x)=\gcd(x,0)=x$ for every non-negative integer $x$. | |
| Lelle and Flamm can decide to stop the match whenever they want, and the final score of the performance is $l \cdot W_L + f \cdot W_F$. | |
| Please help Lelle and Flamm coordinate their wins and losses such that the performance is successful, and the total score of the performance is maximized. | |
| The first line contains an integer $t$ ($1\leq t \leq 10^3$) — the number of test cases. | |
| The only line of each test case contains four integers $n$, $m$, $l$, $f$ ($2\leq n\leq m \leq 2\cdot 10^7$, $1\leq l,f \leq 10^9$, $\bf{n=m}$): $n$, $m$ gives the upper bound on the number of Lelle and Flamm's wins, $l$ and $f$ determine the final score of the performance. | |
| Unusual additional constraint: it is guaranteed that, for each test, there are no pairs of test cases with the same pair of $n$, $m$. | |
| For each test case, output a single integer — the maximum total score of a successful performance. | |
| In the first test case, a possible performance is as follows: | |
| * Flamm wins, $\gcd(0,1)=1$. * Lelle wins, $\gcd(1,1)=1$. * Flamm wins, $\gcd(1,2)=1$. * Flamm wins, $\gcd(1,3)=1$. * Lelle wins, $\gcd(2,3)=1$. * Lelle and Flamm agree to stop the match. | |
| The final score is $2\cdot2+3\cdot5=19$. | |
| In the third test case, a possible performance is as follows: | |
| * Flamm wins, $\gcd(0,1)=1$. * Lelle wins, $\gcd(1,1)=1$. * Lelle wins, $\gcd(2,1)=1$. * Lelle wins, $\gcd(3,1)=1$. * Lell |