[ICPC 2018 Qingdao R] Sequence and Sequence

Luogu

IDLGP9885

Time10000ms

Memory256MB

DifficultyP7

数学2018O2优化ICPC青岛

Consider the following two sequences $P$ and $Q$. We denote $P(i)$ as the $i$-th element in sequence $P$, and $Q(i)$ as the $i$-th element in sequence $Q$: - Sequence $P$ is a $\textbf{sorted}$ sequence where for all $k \in \mathbb{Z^+}$, $k$ appears in sequence $P$ for $(k+1)$ times ($\mathbb{Z^+}$ is the set of all positive integers). That is to say, $P = \{1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, \dots \}$ - Sequence $Q$ can be derived from the following equations: $$\begin{cases} Q(1) = 1 & \\ Q(i) = Q(i-1) + Q(P(i)) & \text{if } i > 1 \end{cases}$$ That is to say, $Q = \{1, 2, 4, 6, 8, 12, 16, 20, 24, 30, 36, 42, 48, 54, 62, \dots \}$ ![](https://cdn.luogu.com.cn/upload/image_hosting/ukq7qs74.png) Given a positive integer $n$, please calculate the value of $Q(n)$. ## Input There are multiple test cases. The first line of the input contains an integer $T$ (about $10^4$), indicating the number of test cases. For each test case: The first and only line contains an integer $n$ ($1 \le n \le 10^{40}$). ## Output For each test case output one line containing one integer, indicating the value of $Q(n)$. [samples]

Samples

Input #1

4
10
100
1000
987654321123456789

Output #1

30
2522
244274
235139898689017607381017686096176798

API Response (JSON)

{
  "problem": {
    "name": "[ICPC 2018 Qingdao R] Sequence and Sequence",
    "description": {
      "content": "Consider the following two sequences $P$ and $Q$. We denote $P(i)$ as the $i$-th element in sequence $P$, and $Q(i)$ as the $i$-th element in sequence $Q$: - Sequence $P$ is a $\\textbf{sorted}$ seque",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 10000,
      "memory_limit": 262144
    },
    "difficulty": {
      "LuoguStyle": "P7"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9885"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider the following two sequences $P$ and $Q$. We denote $P(i)$ as the $i$-th element in sequence $P$, and $Q(i)$ as the $i$-th element in sequence $Q$:\n\n- Sequence $P$ is a $\\textbf{sorted}$ seque...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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