CF721E Road to Home

Once Danil the student was returning home from tram stop lately by straight road of length $ L $ . The stop is located at the point $ x=0 $ , but the Danil's home — at the point $ x=L $ . Danil goes from $ x=0 $ to $ x=L $ with a constant speed and does not change direction of movement. There are $ n $ street lights at the road, each of which lights some continuous segment of the road. All of the $ n $ lightened segments do not share common points. Danil loves to sing, thus he wants to sing his favourite song over and over again during his walk. As soon as non-lightened segments of the road scare him, he sings only when he goes through the lightened segments. Danil passes distance $ p $ while performing his favourite song once. Danil can't start another performance if the segment passed while performing is not fully lightened. Moreover, if Danil has taken a pause between two performances, he is not performing while not having passed a segment of length at least $ t $ . Formally, 1. Danil can start single performance at a point $ x $ only if every point of segment $ [x,x+p] $ is lightened; 2. If Danil has finished performing at a point $ x+p $ , then the next performance can be started only at a point $ y $ such that $ y=x+p $ or $ y>=x+p+t $ satisfying the statement under the point $ 1 $ . Blue half-circles denote performances. Please note that just after Danil has taken a pause in performing, he has not sang for a path of length of at least $ t $ .Determine how many times Danil can perform his favourite song during his walk from $ x=0 $ to $ x=L $ . Please note that Danil does not break a single performance, thus, started singing another time, he finishes singing when having a segment of length of $ p $ passed from the performance start point.

The first line of the input contains four integers $ L $ , $ n $ , $ p $ and $ t $ ( $ 1

Print the only integer — the maximum number of performances of Danil's favourite song on the path from $ x=0 $ to $ x=L $ .

The first sample case is just about corresponding to the picture from the statement.