Traffic Jam

A one-way road has a traffic light. There are $n$ cars waiting on the road, and each driver wants to pass as quickly as possible. Drivers never run a red light, so they must wait for green.

The light has only red and green. Green stays on for $g$ seconds, then red for $r$ seconds, then green again for $g$ seconds, and so on. At the first moment the light is green. A car may pass at the moment the light switches.

It is 7 a.m., and the drivers are sleepy. The $i$-th driver needs $a_i$ seconds to realize that the light is green. The first car in line can start $a_i$ seconds after green begins. Each other car can start $a_i$ seconds after the car in front of it starts moving. Cars move fast, so the time to reach the light and pass through it is ignored. No car passes on red.

Find the time, counted from the first green, at which the last car passes the light.

The first line contains integers $n$ ($1 \le n \le 1000$), $g$, and $r$ ($1 \le g, r \le 10^9$): the number of cars, the green duration, and the red duration, in seconds. The second line contains $n$ integers $a_i$ ($0 \le a_i \le g$): the seconds each driver needs to realize the light is green.

Print one integer: the time at which the last car passes the light.