Fading Wind

You are competing in an outdoor paper airplane flying contest, and you want to predict how far your paper airplane will fly. Your design has a fixed factor $k$. If the airplane's velocity is at least $k$, it rises. If its velocity is less than $k$, it descends.

Here is how your paper airplane flies:

• You start by throwing the airplane with a horizontal velocity of $v$ at a height of $h$. An external wind blows with a strength of $s$.

• While $h > 0$, repeat the following sequence:

  • Increase $v$ by $s$. Then, decrease $v$ by $\max(1, \left\lfloor \frac{v}{10} \right\rfloor)$. Here $\left\lfloor \frac{v}{10} \right\rfloor$ is $\frac{v}{10}$ rounded down to the nearest integer.
  • If $v \ge k$, increase $h$ by one.
  • If $0 < v < k$, decrease $h$ by one. If $h$ is zero after the decrease, set $v$ to zero.
  • If $v \le 0$, set $h$ to zero and $v$ to zero.
  • The airplane now travels horizontally by $v$ units.
  • If $s > 0$, decrease $s$ by $1$.

Compute how far the paper airplane travels horizontally.

The single line of input contains four integers $h$, $k$, $v$, and $s$ $(1 \le h, k, v, s \le 10^3)$, where $h$ is the starting height, $k$ is the fixed factor, $v$ is the starting velocity, and $s$ is the strength of the wind.

Output a single integer, the horizontal distance the airplane travels. The distance is always an integer.