P11132 [MX-X5-T4] "GFOI Round 1" epitaxy

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You are given two positive integers $n, m$. Define the **value** of a permutation $p$ of $1 \sim n$ as the greatest common divisor of the maximum values of all $n - m + 1$ consecutive subarrays of length $m$. (By definition, the greatest common divisor of a single number is the number itself.) Please find a permutation of $1 \sim n$ with the maximum value among all such permutations. If there are multiple, output any one. This problem will use a **custom checker** to verify whether the permutation you construct is correct, so outputting any permutation with the maximum value will be accepted.

**This problem has multiple test cases.** The first line contains a positive integer $T$, denoting the number of test cases. For each test case: The first line contains two positive integers $n, m$.

For each test case, output one line with $n$ positive integers, denoting a permutation $p_1, p_2, \ldots, p_n$ that meets the requirement. This problem will use a **custom checker** to verify whether the permutation you construct is correct, so outputting any permutation with the maximum value will be accepted.

**Sample Explanation.** In the first test case, when $n = 2, m = 2$, the permutation $p = [1, 2]$ has the maximum value, which is $2$. It can also be proven that when $n = 2, m = 2$, there is no permutation with value $> 2$. In the second test case, when $n = 4, m = 2$, the permutation $p = [1, 2, 4, 3]$ has the maximum value, which is $2$, because the maximum values of all subarrays of length $2$ are $2, 4, 4$, whose greatest common divisor is $2$. It can also be proven that when $n = 4, m = 2$, there is no permutation with value $> 2$. **Constraints.** **This problem uses bundled tests and enables subtask dependencies.** | Subtask ID | $n \le$ | $\sum n \le$ | Special Property | Subtask Dependencies | Score | | :-: | :-: | :-: | :-: | :-: | :-: | | $1$ | $8$ | $100$ | None | None | $28$ | | $2$ | $10^6$ | $10^6$ | A | None | $23$ | | $3$ | $10^6$ | $10^6$ | B | None | $7$ | | $4$ | $10^6$ | $10^6$ | None | $1, 2, 3$ | $42$ | - Special Property A: $m = 2$. - Special Property B: $m = n$. For all testdata, it holds that $1 \le T \le 10^5$, $1 \le m \le 10^6$, $2 \le n, \sum n \le 10^6$, and $m \le n$. Translated by ChatGPT 5