Harmonic Mean

AtCoder

IDarc163_c

Time2000ms

Memory256MB

Difficulty—

Determine whether there is a length-$N$ sequence of positive integers $A=(A_1,A_2,\dots,A_N)$ that satisfies all of the following conditions, and if it exists, construct one. * $\sum_{i=1}^{N} \frac{1}{A_i} = 1$ * All elements of $A$ are distinct. * $1 \le A_i \le 10^9(1 \le i \le N)$ You are given $T$ test cases. Find the answer for each of them. ## Constraints * $1 \le T \le 500$ * $1 \le N \le 500$ ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Here, $\mathrm{case}_i$ is the $i$\-th test case. Each test case is given in the following format: $N$ [samples]

Samples

Input #1

2
3
5

Output #1

Yes
2 3 6 
Yes
3 4 5 6 20 

In the first test case, $N=3$.
$A=(2,3,6)$ is valid because $\frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1$ and it satisfies all other conditions.
In the second test case, $N=5$.
$A=(3,4,5,6,20)$ is valid because $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{20} = 1$ and it satisfies all other conditions.
Note that, for example, $A=(5,5,5,5,5)$ satisfies the first and third conditions, but it is invalid because it contains duplicated elements.

API Response (JSON)

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    "description": {
      "content": "Determine whether there is a length-$N$ sequence of positive integers $A=(A_1,A_2,\\dots,A_N)$ that satisfies all of the following conditions, and if it exists, construct one. *   $\\sum_{i=1}^{N} \\fra",
      "description_type": "Markdown"
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    "platform": "AtCoder",
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      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "sign": "arc163_c"
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      "statement_type": "Markdown",
      "content": "Determine whether there is a length-$N$ sequence of positive integers $A=(A_1,A_2,\\dots,A_N)$ that satisfies all of the following conditions, and if it exists, construct one.\n\n*   $\\sum_{i=1}^{N} \\fra...",
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      "language": "English"
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