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: >$N$ $H$\ >$t_1$ $d_1$\ >$\vdots$\ >$t_N$ $d_N$ #### 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.

Print the answer.

***For Sample #1:*** 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 $-1$.

AtCoder [ABC303F]