Slimming Plan

Chokudai loves eating so much. However, his doctor Akensho told him that he was overweight, so he finally decided to lose weight.

Chokudai made a slimming plan with a cycle of $D$ days. It is represented by $D$ integers $w_0, \ldots, w_{D-1}$. His weight is $S$ on day 0 of the plan, and he aims to reduce it to $T \ (S > T)$. If his weight on day $i$ of the plan is $x$, it will be $x + w_{i \% D}$ on day $(i+1)$. Here $i \% D$ is the remainder obtained by dividing $i$ by $D$. If his weight gets less than or equal to $T$, he stops slimming immediately.

If his slimming plan takes too many days or never ends, he should reconsider it.

Determine whether it ends, and report how many days it takes if it ends.

The input consists of a single test case formatted as follows.

S T D
w0⋯wD−1

The first line consists of three integers $S, T, D \ (1 \le S,T,D \le 100{,}000, \ S > T)$. The second line consists of $D$ integers $w_0, \ldots, w_{D-1}$ ($-100{,}000 \le w_i \le 100{,}000$ for each $i$).

If Chokudai's slimming plan ends on the $d$-th day, print $d$ in one line. If it never ends, print $-1$.