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.

The input is given from Standard Input in the following format:

```
$N$ $H$
$t_1$ $d_1$
$\vdots$
$t_N$ $d_N$
```

Print the answer.

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

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.