Superhero Battle

题意翻译

       超级英雄与怪物搏斗。这场战斗由几轮组成，每轮持续时间正好是 n 分钟。一轮结束后，下一轮马上开始。这是一次又一次的重复。        每一轮都是相同的攻击方式。它由 n 个数字描述：d1 , d2 ,…,dn（−10^6 ≤ di ≤ 10^6）。第 i 个数意味着怪物的生命值在每轮的第 i 分钟变化 di 值。也就是说，如果在第 i 分钟之前怪物的生命值是 h，那么在第 i 分钟之后它会变为 h+di。        怪物的初始生命值是 H 。输出怪物哪一分钟死亡。如果怪物的生命值小于或等于0，怪物就会死亡。如果战斗无限持续，则输出-1。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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.

输入输出样例

输入样例 #1

1000 6
-100 -200 -300 125 77 -4

输出样例 #1

9

输入样例 #2

1000000000000 5
-1 0 0 0 0

输出样例 #2

4999999999996

输入样例 #3

10 4
-3 -6 5 4

输出样例 #3

-1