Description

You are playing a game. The goal of this game is to kill the monster when you are still alive (HP > 0, HP = health point). The monster is dead if and only if its HP <= 0.

This game consists of rounds, and you go first in each round.

You have 3 options in each round:

1. ATTACK. This will deduct the monster's HP. If your damage point is p, then you can deduct p monster's HP.
2. HEAL. You can recover some of your HP, but it can't exceed your max HP.
3. Level-up. Level-up might enhance the effect of attacking or healing, but if you are not lucky enough, sometimes it will deduct the effect of attacking and healing. Thus, choosing to level-up is not always a good choice. If you have reached max level, taking this action makes no effect.

In each round, the monster will attack you once with a fixed amount of damage points.

You start the game with full HP and level 1. What is the minimun number of rounds you need to kill the monster?

Input

First line contains 4 numbers L, HP, MHP, MDMG.

• L = max level
• HP = your max HP
• MHP = monster's HP in the beginning of game
• MDMG = monster's damage point

Each of the next L lines describes each level, i-th line of them describing level i. Each of them consists of two numbers, DMG and HL.

• DMG = your damage point when you use ATTACK at level i
• HL = amount of HP you can recover when you use HEAL at level i

---

Limits:

• L <= 15
• HP <= 300
• MHP <= 400
• MDMG <= 10000
• DMG <= 10000
• HL <= 50

Output

Print a single integer, denoting the mininum number of steps you need to kill the monster.

If you are unable to beat the monster, print -1.

Sample Input  Download

Sample Output  Download

Tags

Discuss