There is only one elevator in the tall building with N floors. The parking for this building is at the basement floor which is located under the first floor. All floors are enumerated from 1 to N, growing up. At i-th floor there are A_i people who wish to descend from the floor to parking. You know that the elevator is unable to carry more than C people at any time. Descending or ascending one floor takes P seconds. Your task is to find the maximum possible number of people the elevator may deliver to parking within T seconds of operation, if it is located at the parking in the beginning. You may assume that stopping at a stage to load or unload people is done instantly.

In the first line of input file there are four integers N, C, P, T (1 ≤ N ≤ 100, 1 ≤ C ≤ 10⁹, 1 ≤ P ≤ 10⁹, 1 ≤ T ≤ 10⁹). The second line contains the sequence of N integers A₁, A₂,..., A_N (0 ≤ A_i ≤ 10⁹). The sum of all A_i does not exceed 10⁹ too.

Output the maximum possible number of people who can reach the parking.

sample input	sample output
4 5 2 15 0 1 2 3	3

sample input	sample output
4 5 2 18 0 1 2 3	5

sample input	sample output
3 2 1 9 1 1 1	3