+ محدودیت زمان: ۱ ثانیه + محدودیت حافظه: ۲۵۶ مگابایت ---------- Nowadays everything depends on exchange rate of dollar (Now it is called *rate* due to its importance). Total atmosphere of our country has been affected by *rate*. But this is not the only reason of economical disorders. Some of sellers called "*traitors*" cause the other reason. These sellers act different in different rate swings: + In rate increment, they increase the price of goods bought before and pretext: "I must increase because I need to buy this good again". + In rate decrement, they don't decrease the price of goods bought before and pretext: "I paid more and decrement has lots of damages for me”. Actually if *rate* changes from $r_1$ to $r_2$ (and $r_2 > r_1$ ), *traitors* multiply their price to $\frac{r_2}{r_1}$ and round the product to the nearest(if distances were equal, to upper nearest) multiple of *round base*. For example if a *traitor* bought a pen $1000_{Rials}\space$ in first day and *rate* changed from $8000_{Rials}\space$ to $23000_{Rials}$ and then to $12000_{Rials}\space$, and round base was $100_{Rials}\space$, finally he sells this pen $2900_{Rials}\space$. because: $100 \times 28 < 1000 \times \frac{23000}{8000} = 2875 \le 100 \times 29$ and $2875$ is closer to $2900$. Ali wants to buy a battery for his laptop. But there is only one shop selling this kind of battery. Ali knows that this shop's seller is a *traitor* and has this battery since **n** days ago. Ali went to this shop and realised that the seller sells the battery **p** Rials and round base for this shop is **b** Rials. Ali wants to know how much was this battery's price **d** days ago. He is busy preparing problems for SBU Newbies Contest so he needs your help. # ورودی The input file contains several input sets. The description of each set is given below: Each set starts with four integers $n (0 ≤ n ≤ 10^5)$, the number of days passed from seller's buy, $p (0 ≤ p ≤ 10^9)$, the price of battery, $b (1 ≤ b ≤ 10^5)$, round base, and $d (0 ≤ d ≤ n)$, the number of days passed from Ali's slightly day, following a line with $n + 1$ non-negative space separated integers $r_0, r_1, \dots, r_n\space$. $r_i$ equals the rate when $i$ days passed from seller's buy. Actually $r_0$ equals the rate when seller bought the battery. It is guaranteed that Input will follow the descriptions given.Input is terminated by a set where $n=p=b=d=0$ which should not be processed. There is a blank line between two input sets. sum of $n$ over all input sets are at most $2\times 10^5$ and count of input sets are less than $20$. # خروجی For each input set, produce one line of output including space separated $m$ and $M$ which respectively mean the least and the most possible prices the battery could have in d days ago. # مثال‌ها ## ورودی نمونه ۱ ``` 1 15000 1000 1 8000 12000 2 45000 1000 2 8000 36000 12000 3 20 4 1 1 5 4 3 0 0 0 0 ``` ## خروجی نمونه ۱ ``` 9667 10333 9889 10111 20 20 ```