Score : $100$ points

问题描述

Takahashi 在他第 $N$ 个生日时，身高为 $T$ 厘米。
另外，我们还知道以下事实：

• 在从 Takahashi 出生（0岁生日）到第 $X$ 个生日的每一年中，他的身高增长了 $D$ 厘米。更正式地讲，对于每个 $i = 1, 2, \ldots, X$，他在从第 $(i-1)$ 个生日到第 $i$ 个生日之间身高增加了 $D$ 厘米。
• 在 Takahashi 的第 $X$ 个生日和第 $N$ 个生日之间，他的身高没有发生变化。

求 Takahashi 在他第 $M$ 个生日时的身高，以厘米为单位。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi had his $N$-th birthday, when he was $T$ centimeters tall.
Additionally, we know the following facts:

• In each year between Takahashi's birth ($0$-th birthday) and his $X$-th birthday, his height increased by $D$ centimeters. More formally, for each $i = 1, 2, \ldots, X$, his height increased by $D$ centimeters between his $(i-1)$-th birthday and his $i$-th birthday.
• Between Takahashi's $X$-th birthday and his $N$-th birthday, his height did not change.

Find Takahashi's height on his $M$-th birthday, in centimeters.

Constraints

• $0 \leq M \lt N \leq 100$
• $1 \leq X \leq N$
• $1 \leq T \leq 200$
• $1 \leq D \leq 100$
• Takahashi was at least $1$ centimeter tall at his birth.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $X$ $T$ $D$

Output

Print the answer as an integer.

Sample Input 1

38 20 17 168 3

Sample Output 1

168

In this sample, Takahashi was $168$ centimeters tall on his $38$-th birthday. Also, his height did not change between his $17$-th birthday and $38$-th birthday.
From these facts, we find that he was $168$ centimeters tall on his $20$-th birthday, so the answer is $168$.

Sample Input 2

1 0 1 3 2

Sample Output 2

1

In this sample, Takahashi was $1$ centimeter tall on his $0(=M)$-th birthday and $3(=T)$ centimeters tall on his $1(=N)$-st birthday.

Sample Input 3

100 10 100 180 1

Sample Output 3

90

update @ 2024/3/10 10:58:59