Fried Soboro Buns

Yeongseon came back from Daejeon with $n$ fried soboro buns.

She left them in the club room to share with the members and stepped out for a moment. When she got back, $s$ buns were untouched. A bun that someone had picked up to eat does not count among those $s$.

While Yeongseon was away, $m$ people were in the room, numbered $1$ to $m$. She eats with the members often, so she knows $t_i$, the number of seconds person $i$ needs to eat one bun.

Everyone picks up a bun the moment Yeongseon leaves, at second $0$, and picks up the next bun as soon as the one in hand is finished. So person $i$ picks up a bun at seconds $0$, $t_i$, $2t_i$, $3t_i$, and so on. When several people pick at the same moment, the person with the smaller number picks first.

Find the number of the person who picked up a bun last.

For example, suppose person $1$ eats one bun in $1$ second, person $2$ in $3$ seconds, person $3$ in $5$ seconds, and there are $1000$ buns.

• If $1$ bun is gone, person $1$ picked up a first bun.
• If $2$ are gone, person $2$ picked up a first bun right after person $1$.
• If $3$ are gone, person $3$ picked up a first bun right after person $2$.
• If $4$ are gone, person $1$ finished the bun in hand and picked up a second one.
• If $5$ are gone, person $1$ picked up a third bun.
• If $6$ are gone, person $1$ picked up a fourth bun.
• If $7$ are gone, person $2$ finished the bun in hand and picked up a second one right after person $1$.

The first line contains $n$ and $s$ separated by a space. $n$ is the number of buns Yeongseon bought ($1 \le n \le 100000$), and $s$ is the number of untouched buns left when she returned ($0 \le s \le n-1$).

The second line contains the number of people $m$ ($1 \le m \le 100000$). Each of the next $m$ lines contains $t_i$, the number of seconds one person needs to eat one bun, given for person $1$ through person $m$ in order ($1 \le t_i \le 1000$).

Print the number of the person who picked up a bun last.