Interval Counts

AtCoder

IDarc166_d

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $x_1, \ldots, x_N$ such that $x_1 < \cdots < x_N$, and positive integers $y_1, \ldots, y_N$. Consider a tuple $(M, L_1, R_1, \ldots, L_M, R_M)$ that satisfies all of the following conditions. * $M$ is a positive integer. * For each $j \ (1\leq j\leq M)$, $L_j$ and $R_j$ are integers such that $L_j\leq R_j$. * For each $i \ (1\leq i\leq N)$, exactly $y_i$ integers $j \ (1\leq j\leq M)$ satisfy $L_j\leq x_i\leq R_j$. It can be proved that such a tuple always exists. Find the maximum value of $\min \lbrace R_j-L_j\mid 1\leq j\leq M\rbrace$ for such a tuple. If there is no maximum value, print `-1`. ## Constraints * $1\leq N\leq 2\times 10^5$ * $1\leq x_1 < \cdots < x_N \leq 10^9$ * $1\leq y_i \leq 10^9$ ## Input The input is given from Standard Input in the following format: $N$ $x_1$ $\cdots$ $x_N$ $y_1$ $\cdots$ $y_N$ [samples]

Samples

Input #1

3
1 3 5
1 3 1

Output #1

2

For example, we have $\min \lbrace R_j-L_j\mid 1\leq j\leq M\rbrace = 2$ for the tuple $(3, 1, 4, 2, 4, 3, 5)$.

Input #2

3
1 10 100
2 3 2

Output #2

\-1

For example, we have $\min \lbrace R_j-L_j\mid 1\leq j\leq M\rbrace = 990$ for the tuple $(3, -1000, 10, -1000, 1000, 10, 1000)$. There is no maximum value of $\min \lbrace R_j-L_j\mid 1\leq j\leq M\rbrace$.

Input #3

7
10 31 47 55 68 73 90
3 7 4 6 3 4 4

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Interval Counts",
    "description": {
      "content": "You are given positive integers $x_1, \\ldots, x_N$ such that $x_1 < \\cdots < x_N$, and positive integers $y_1, \\ldots, y_N$. Consider a tuple $(M, L_1, R_1, \\ldots, L_M, R_M)$ that satisfies all of th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc166_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given positive integers $x_1, \\ldots, x_N$ such that $x_1 < \\cdots < x_N$, and positive integers $y_1, \\ldots, y_N$.\nConsider a tuple $(M, L_1, R_1, \\ldots, L_M, R_M)$ that satisfies all of th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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