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code_segments/segment_397.txt

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+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