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.

Input format:
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.
Output format:
For each test case, output the minimum number of coins needed to defeat the monster.
Example Input 0:
4
2 3 5 5
10 20 40 5
1 60 100 10
60 1 100 10

Example Output 0:
12
190
280
160

Notes:
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 a total of $$$5 + 35 = 40$$$ damage, defeating the monster who has exactly $$$40$$$ health. The total number of coins you use is $$$50 + 20 + 20 + 100 = 190$$$ coins.

Example input:
4
2 3 5 5
10 20 40 5
1 60 100 10
60 1 100 10


Example output:
12
190
280
160