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.

Input

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 $*d*$.

Output

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

Note

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.