405044: GYM101754 C World of Darkraft 3

Roma plays a new version of the "World of Darkraft" game as a wizard character. Roma values his time and tries to complete in-game tasks as efficient as possible.

Roma is now fighting n monsters. The i-th of these monsters has h_i health points. A monster dies when his health points become zero of negative (at that moment Roma's character gains experience).

Roma's character has a pool of m mana points. The character possesses two spell abilities: "Lightning strike" and "Ring of ice".

• "Lightning strike" spell deals d_s damage to a chosen monster (that is, descreases its health points by d_s), and one cast of this spell costs c_s mana points.
• "Ring of ice" spell deals d_a damage to all monsters still alive, and one cast of this spell costs c_a mana points.

The character can not use a spell if the number of mana points left is strictly less than the cost of this spell. The battle finishes as soon as all monsters are dead, or if it is not possible to cast any of two spells (then the character needs to retreat and rest).

In this battle Roma wants to gain as much experience as possible. Help Roma determine the maximum possible number of monsters he can kill.

The first line contains six integers n, m, d_s, c_s, d_a and c_a (1 ≤ n, m, d_s, c_s, d_a, c_a ≤ 100) — the number of monsters, the amount of characters' mana, and also damage and mana cost of "Lightning strike" and "Ring of ice" spells respectively.

The second line contains n integers h₁, h₂, ..., h_n — monsters' health points (1 ≤ h_i ≤ 100).

Print one number — the maximum number of monsters that can be defeated.

3 5 1 1 3 3
4 1 5

2

5 70 10 10 1 20
11 11 11 11 11

5

In the first sample, the character can cast "Ring of ice" once (as a result, the first monster will have one health point, the third monster will have two health points, and the second monster will die). After that, the character can apply "Lightning strike" twice to kill another monster.

In the second sample, the only way to defeat all monsters is to cast "Ring of ice" once, and "Lightning strike" once for each monster.