Problem Statement

A monster with health H has appeared in front of you, and a turn-based battle has started.
In each turn 1,2,…, you cast one of N spells, spells 1,…,N.
If you cast spell i in turn j, the monster's health reduces by d_i in each turn j,j+1,…,j+t_i －1.
Find the earliest turn that you can make the monster's health 0 or less.

Input

The input is given from Standard Input in the following format:
N H
t_1 d_1
$\vdots$
t_N d_N

Output

Print the answer.

Constraints

• $1 \leq N \leq 3 \times 10^5$
• $1 \leq H \leq 10^{18}$
• $1 \leq t_i,d_i \leq 10^9$
• All values in the input are integers.

Sample Input 1

2 20
2 2
5 1

Sample Output 1

6

The following procedure makes the monster's health 0 or less in turn 6, which is the earliest.

• Cast spell 1 in turn 1. Due to the spell cast in turn 1, the monster's health reduces by 2 and becomes 18.
• Cast spell 2 in turn 2. Due to the spells cast in turns 1 and 2, the monster's health reduces by 2+1=3 and becomes 15.
• Cast spell 1 in turn 3. Due to the spells cast in turns 2 and 3, the monster's health reduces by 1+2=3 and becomes 12.
• Cast spell 2 in turn 4. Due to the spells cast in turns 2,3 and 4, the monster's health reduces by 1+2+1=4 and becomes 8.
• Cast spell 1 in turn 5. Due to the spells cast in turns 2,4 and 5, the monster's health reduces by 1+1+2=4 and becomes 4.
• Cast spell 2 in turn 6. Due to the spells cast in turns 2,4,5 and 6, the monster's health reduces by 1+1+2+1=5 and becomes -1.

Sample Input 2

10 200
1 21
1 1
1 1
8 4
30 1
3 1
10 2
8 1
9 1
4 4

Sample Output 2

9

见题面 Input 部分

见题面 Output 部分