| Man, this Genshin boss is so hard. Good thing they have a top-up of $6$ coins for only $ \$4.99$. I should be careful and spend no more than I need to, lest my mom catches me... | |
| You are fighting a monster with $z$ health using a weapon with $d$ damage. Initially, $d=0$. You can perform the following operations. | |
| * Increase $d$ — the damage of your weapon by $1$, costing $x$ coins. * Attack the monster, dealing $d$ damage and costing $y$ coins. | |
| You cannot perform the first operation for more than $k$ times in a row. | |
| Find the minimum number of coins needed to defeat the monster by dealing at least $z$ damage. | |
| The first line contains a single integer $t$ ($1\le t\le 100$) — the number of test cases. | |
| The only line of each test case contains 4 integers $x$, $y$, $z$, and $k$ ($1\leq x, y, z, k\leq 10^8$) — the first operation's cost, the second operation's cost, the monster's health, and the limitation on the first operation. | |
| For each test case, output the minimum number of coins needed to defeat the monster. | |
| In the first test case, $x = 2$, $y = 3$, $z = 5$, and $k = 5$. Here's a strategy that achieves the lowest possible cost of $12$ coins: | |
| * Increase damage by $1$, costing $2$ coins. * Increase damage by $1$, costing $2$ coins. * Increase damage by $1$, costing $2$ coins. * Attack the monster, dealing $3$ damage, costing $3$ coins. * Attack the monster, dealing $3$ damage, costing $3$ coins. | |
| You deal a total of $3 + 3 = 6$ damage, defeating the monster who has $5$ health. The total number of coins you use is $2 + 2 + 2 + 3 + 3 = 12$ coins. | |
| In the second test case, $x = 10$, $y = 20$, $z = 40$, and $k = 5$. Here's a strategy that achieves the lowest possible cost of $190$ coins: | |
| * Increase damage by $5$, costing $5\cdot x$ = $50$ coins. * Attack the monster once, dealing $5$ damage, costing $20$ coins. * Increase damage by $2$, costing $2\cdot x$ = $20$ coins. * Attack the monster $5$ times, dealing $5\cdot 7 = 35$ damage, costing $5\cdot y$ = $100$ coins. | |
| You deal |