Christmas is coming up, and Santa needs to finish wrapping all his presents! He must purchase equipment to establish some assembly lines and hire ~K~ elves to operate them. When hiring elves, Santa can either place them at an already existing assembly line, or he can open up a new assembly line and place the elf there. The cost of hiring the ~i^{th}~ elf to work at the ~j^{th}~ assembly line is ~A\cdot i+B\cdot j~. Although Santa only has space for up to ~N~ assembly lines, he can have an unlimited number of elves working at any assembly line. What is the minimum total cost required to hire all ~K~ elves?

Input Specification

One line, containing four integers ~N,K,A,B~

Output Specification

Output the minimum total cost. Note that this number may be too large for a ~32~-bit integer.

Constraints

Subtask 1 [15%]

~1\leq N\leq K\leq 10^3~

~1\leq A,B\leq 10^5~

Subtask 2 [85%]

~1\leq N\leq K\leq 10^6~

~1\leq A,B\leq 10^9~

Sample Input 1

10 6 3 4

Output for Sample Input 1

70

Explanation of Output for Sample Input 1

Consider the following table, where the number in each cell represents the cost for hiring the ~i^{th}~ elf to work at the ~j^{th}~ assembly line. As a reminder, cost = ~3\cdot i + 4\cdot j~.

	~j=1~	~j=2~	~j=3~	~j=4~	~j=5~
~i=1~	~7~	~11~	~15~	~19~	~23~
~i=2~	~10~	~14~	~18~	~22~	~26~
~i=3~	~13~	~17~	~21~	~25~	~29~
~i=4~	~16~	~20~	~24~	~28~	~32~
~i=5~	~19~	~23~	~27~	~31~	~35~
~i=6~	~22~	~26~	~30~	~34~	~38~

The minimum cost to hire ~6~ elves is shown by the boxed numbers. ~7+10+11+13+14+15=70~.

Sample Input 2

3 5 4 2

Output for Sample Input 2

46