A9780. Covered Path

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.

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 $d$ .

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

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.