Recursion - 2#11249

Recursion - 2

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Easy

Three integers $a, b, c$ a, b, c are given. For a given integer $n$ , compute the value of the function:

f (n) = {a, f (n - 1) + bn + c, n = 0 n > 0

f(n) = \begin{cases} a, & n = 0 \\ f(n - 1) + bn + c, & n > 0 \end{cases}

Input

Four integers $a, b, c (∣ a ∣, ∣ b ∣, ∣ c ∣ \leq 1000), n (0 \leq n \leq 1000)$ a, b, c~(|a|, |b|, |c| \le 1000), n~(0 \le n \le 1000).

Print the value of $f (n)$ .

Example 1

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a, b, c

f (n) = {a, f (n - 1) + bn + c, n = 0 n > 0

a, b, c (∣ a ∣, ∣ b ∣, ∣ c ∣ \leq 1000), n (0 \leq n \leq 1000)