P11296 [NOISG 2018 Prelim] Snail

Translated from [NOISG 2018 Prelim A. Snail](https://github.com/noisg/sg_noi_archive/tree/master/2018_prelim).

A snail is trapped in a well of height $H$. The snail keeps trying to climb out of the well. Specifically, in one day the snail goes through $N$ stages. In stage $i$, it climbs $P_i$ meters toward the top of the well (**can be negative**). When the snail’s height is **greater than or equal to** the height of the well opening, it leaves the well. When the snail’s height is less than $0$, its height is considered to be $0$. You are asked to find the earliest time when the snail leaves the well, or report that there is no solution. **Note that both days and stages are 0-indexed, meaning the first stage is actually stage $0$. Also, you may need to use `long long` to store the input numbers.**

The first line contains two integers $H, N$. The next line contains $N$ integers, where the $i$-th integer represents $P_i$.

Output one line with two integers $D, P$, meaning the snail leaves the well on day $D$ at stage $P$. If it can never leave, output `-1 -1`.

### Sample #1 Explanation At stage $0$ on day $0$, it climbs $1$ meter, reaching a total height of $1$ meter. At stage $0$ on day $1$, it climbs $1$ meter, reaching a total height of $2$ meters. At stage $0$ on day $2$, it climbs $1$ meter, reaching a total height of $3$ meters, and leaves the well. ### Sample #2 Explanation Clearly, the snail can never leave. ### Constraints | Subtask | Score | Special Properties | | :----------: | :----------: | :----------: | | $0$ | $0$ | Samples | | $1$ | $11$ | $N = 1$ | | $2$ | $9$ | All $P_i$ are the same | | $3$ | $25$ | $H\times N \leq 10^4$ | | $4$ | $17$ | $P_i\geq0$ | | $5$ | $38$ | None | For $100\%$ of the testdata: $1 \leq H \leq 10^{12}, -10^{12}\leq P_i\leq 10^{12}, 1\leq N \leq 10^4$. Translated by ChatGPT 5