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D - Katana Thrower

Score : $400$ points

Problem Statement

You are going out for a walk, when you suddenly encounter a monster. Fortunately, you have $N$ katana (swords), Katana $1$, Katana $2$, $…$, Katana $N$, and can perform the following two kinds of attacks in any order:

• Wield one of the katana you have. When you wield Katana $i$ $(1 ≤ i ≤ N)$, the monster receives $a_i$ points of damage. The same katana can be wielded any number of times.
• Throw one of the katana you have. When you throw Katana $i$ $(1 ≤ i ≤ N)$ at the monster, it receives $b_i$ points of damage, and you lose the katana. That is, you can no longer wield or throw that katana.

The monster will vanish when the total damage it has received is $H$ points or more. At least how many attacks do you need in order to vanish it in total?

Constraints

• $1 ≤ N ≤ 10^5$
• $1 ≤ H ≤ 10^9$
• $1 ≤ a_i ≤ b_i ≤ 10^9$
• All input values are integers.

Input

Input is given from Standard Input in the following format:

$N$ $H$

$a_1$ $b_1$

$:$

$a_N$ $b_N$

Output

Print the minimum total number of attacks required to vanish the monster.

1 10
3 5

3

You have one katana. Wielding it deals $3$ points of damage, and throwing it deals $5$ points of damage. By wielding it twice and then throwing it, you will deal $3 + 3 + 5 = 11$ points of damage in a total of three attacks, vanishing the monster.

2 10
3 5
2 6

2

In addition to the katana above, you also have another katana. Wielding it deals $2$ points of damage, and throwing it deals $6$ points of damage. By throwing both katana, you will deal $5 + 6 = 11$ points of damage in two attacks, vanishing the monster.

4 1000000000
1 1
1 10000000
1 30000000
1 99999999

860000004

5 500
35 44
28 83
46 62
31 79
40 43

9