{"raw_statement":[{"iden":"problem statement","content":"There are two $100$\\-story buildings, called `A` and `B`. (In this problem, the ground floor is called the first floor.)\nFor each $i = 1,\\dots, 100$, the $i$\\-th floor of `A` and that of `B` are connected by a corridor. Also, for each $i = 1,\\dots, 99$, there is a corridor that connects the $(i+1)$\\-th floor of `A` and the $i$\\-th floor of `B`. You can traverse each of those corridors in both directions, and it takes you $x$ minutes to get to the other end.\nAdditionally, both of the buildings have staircases. For each $i = 1,\\dots, 99$, a staircase connects the $i$\\-th and $(i+1)$\\-th floors of a building, and you need $y$ minutes to get to an adjacent floor by taking the stairs.\nFind the minimum time needed to reach the $b$\\-th floor of `B` from the $a$\\-th floor of `A`."},{"iden":"constraints","content":"*   $1 \\leq a,b,x,y \\leq 100$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$a$ $b$ $x$ $y$"},{"iden":"sample input 1","content":"2 1 1 5"},{"iden":"sample output 1","content":"1\n\nThere is a corridor that directly connects the $2$\\-nd floor of `A` and the $1$\\-st floor of `B`, so you can travel between them in $1$ minute. This is the fastest way to get there, since taking the stairs just once costs you $5$ minutes."},{"iden":"sample input 2","content":"1 2 100 1"},{"iden":"sample output 2","content":"101\n\nFor example, if you take the stairs to get to the $2$\\-nd floor of `A` and then use the corridor to reach the $2$\\-nd floor of `B`, you can get there in $1+100=101$ minutes."},{"iden":"sample input 3","content":"1 100 1 100"},{"iden":"sample output 3","content":"199\n\nUsing just corridors to travel is the fastest way to get there."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}