Numbers on a Circle

AtCoder

IDagc037_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ positive integers arranged in a circle. Now, the $i$\-th number is $A_i$. Takahashi wants the $i$\-th number to be $B_i$. For this objective, he will repeatedly perform the following operation: * Choose an integer $i$ such that $1 \leq i \leq N$. * Let $a, b, c$ be the $(i-1)$\-th, $i$\-th, and $(i+1)$\-th numbers, respectively. Replace the $i$\-th number with $a+b+c$. Here the $0$\-th number is the $N$\-th number, and the $(N+1)$\-th number is the $1$\-st number. Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required. ## Constraints * $3 \leq N \leq 2 \times 10^5$ * $1 \leq A_i, B_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ $B_1$ $B_2$ $...$ $B_N$ [samples]

Samples

Input #1

3
1 1 1
13 5 7

Output #1

4

Takahashi can achieve his objective by, for example, performing the following operations:

*   Replace the second number with $3$.
*   Replace the second number with $5$.
*   Replace the third number with $7$.
*   Replace the first number with $13$.

Input #2

4
1 2 3 4
2 3 4 5

Output #2

\-1

Input #3

5
5 6 5 2 1
9817 1108 6890 4343 8704

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Numbers on a Circle",
    "description": {
      "content": "There are $N$ positive integers arranged in a circle. Now, the $i$\\-th number is $A_i$. Takahashi wants the $i$\\-th number to be $B_i$. For this objective, he will repeatedly perform the following ope",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc037_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ positive integers arranged in a circle.\nNow, the $i$\\-th number is $A_i$. Takahashi wants the $i$\\-th number to be $B_i$. For this objective, he will repeatedly perform the following ope...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments