Fizz Buzz Difference

AtCoder

IDarc166_e

Time10000ms

Memory256MB

Difficulty—

You are given positive integers $n$, $a$, and $b$ such that $a<b$. An integer pair $(L,R)$ such that $1\leq L\leq R$ is said to be a **good pair** when the following condition holds. * Let $n_a$ and $n_b$ be respectively the number of multiples of $a$ and the number of multiples of $b$ among the integers between $L$ and $R$, inclusive. Then, $n_a - n_b = n$. It can be proved that a good pair always exists. Report the good pair with the largest value of $R-L$. If multiple such pairs exist, report the one with the smallest $L$ (from $1\leq L$, the sought $(L, R)$ with the smallest $L$ exists and is unique). You have $T$ test cases to solve. ## Constraints * $1\leq T\leq 2\times 10^5$ * $1\leq n \leq 10^6$ * $1\leq a < b \leq 10^6$ ## Input The input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\vdots$ $\text{case}_T$ Each test case is given in the following format: $n$ $a$ $b$ [samples]

Samples

Input #1

1
3 3 5

Output #1

4 35

$(L,R)=(4,35)$ is a good pair since $n_a=10, n_b=7$.
Some other good pairs are $(1,26)$ and $(10,41)$. $(1,26)$ is not the answer because it does not have the largest $R-L$. $(10,41)$ is not the answer because, although it has the largest $R-L$, it does not have the smallest $L$.

Input #2

5
4 3 5
6 2 4
1 1 2
123 456 789
9876 54 321

Output #2

10 50
3 29
2 4
5473 140447
163 641411

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "You are given positive integers $n$, $a$, and $b$ such that $a<b$.\nAn integer pair $(L,R)$ such that $1\\leq L\\leq R$ is said to be a **good pair** when the following condition holds.\n\n*   Let $n_a$ an...",
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