CF1141E Superhero Battle

A superhero fights with a monster. The battle consists of rounds, each of which lasts exactly $ n $ minutes. After a round ends, the next round starts immediately. This is repeated over and over again. Each round has the same scenario. It is described by a sequence of $ n $ numbers: $ d_1, d_2, \dots, d_n $ ( $ -10^6 \le d_i \le 10^6 $ ). The $ i $ -th element means that monster's hp (hit points) changes by the value $ d_i $ during the $ i $ -th minute of each round. Formally, if before the $ i $ -th minute of a round the monster's hp is $ h $ , then after the $ i $ -th minute it changes to $ h := h + d_i $ . The monster's initial hp is $ H $ . It means that before the battle the monster has $ H $ hit points. Print the first minute after which the monster dies. The monster dies if its hp is less than or equal to $ 0 $ . Print -1 if the battle continues infinitely.

The first line contains two integers $ H $ and $ n $ ( $ 1 \le H \le 10^{12} $ , $ 1 \le n \le 2\cdot10^5 $ ). The second line contains the sequence of integers $ d_1, d_2, \dots, d_n $ ( $ -10^6 \le d_i \le 10^6 $ ), where $ d_i $ is the value to change monster's hp in the $ i $ -th minute of a round.

Print -1 if the superhero can't kill the monster and the battle will last infinitely. Otherwise, print the positive integer $ k $ such that $ k $ is the first minute after which the monster is dead.