Covered Path

题面翻译

题目描述：

小 $P$ 用车载计算机测量出，汽车在某段路径的起点速度为 $v_1$ 米/秒，终点速度为 $v_2$ 米/秒，我们知道这段路需要 $t$ 秒通过。假设每秒内的速度恒定，每秒之间速度的差值不超过 $d$ 。求路径段的最大可能长度，单位为米。

输入格式：

第一行包含两个整数 $v_1$ 和 $v_2$ （$1\le v_1,v_2\le 100$），第二行包含两个整数 $t$ 和 $d$ （$2\le t\le 100$，$0\le d\le 10$），保证一定有解。

输出格式：

仅有一个数，表示以米为单位的路径最大可能长度。

样例解释：

在样例1中，小 $P$ 的车的速度序列如下：5、7、8、6。因此，总路径是 $5+7+8+6=265+7+8+6=26$ 米。

题目描述

The on-board computer on Polycarp's car measured that the car speed at the beginning of some section of the path equals $v_{1}$ meters per second, and in the end it is $v_{2}$ meters per second. We know that this section of the route took exactly $t$ seconds to pass.

Assuming that at each of the seconds the speed is constant, and between seconds the speed can change at most by $d$ meters per second in absolute value (i.e., the difference in the speed of any two adjacent seconds does not exceed $d$ in absolute value), find the maximum possible length of the path section in meters.

输入格式

The first line contains two integers $v_{1}$ and $v_{2}$ ( $1<=v_{1},v_{2}<=100$ ) — the speeds in meters per second at the beginning of the segment and at the end of the segment, respectively.

The second line contains two integers $t$ ( $2<=t<=100$ ) — the time when the car moves along the segment in seconds, $d$ $(0<=d<=10)$ — the maximum value of the speed change between adjacent seconds.

It is guaranteed that there is a way to complete the segment so that:

• the speed in the first second equals $v_{1}$ ,
• the speed in the last second equals $v_{2}$ ,
• the absolute value of difference of speeds between any two adjacent seconds doesn't exceed $d$ .

输出格式

Print the maximum possible length of the path segment in meters.

样例 #1

样例输入 #1

5 6
4 2

样例输出 #1

26

样例 #2

样例输入 #2

10 10
10 0

样例输出 #2

100

提示

In the first sample the sequence of speeds of Polycarpus' car can look as follows: 5, 7, 8, 6. Thus, the total path is $5+7+8+6=26$ meters.

In the second sample, as $d=0$ , the car covers the whole segment at constant speed $v=10$ . In $t=10$ seconds it covers the distance of 100 meters.