Covered Path

1000ms

262144K

Description:

The on-board computer on Polycarp's car measured that the car speed at the beginning of some section of the path equals v₁ meters per second, and in the end it is v₂ 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 v₁ and v₂ (1 ≤ v₁, v₂ ≤ 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 v₁,
the speed in the last second equals v₂,
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.

Sample Input:

5 6
4 2

Sample Output:

Sample Input:

10 10
10 0

Sample Output:

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.

Informação

Provedor Codeforces

Código CF534B