Hi Codeforces,↵
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Can anybody help me with the following <a href="https://www.codechef.com/ACMAMR15/problems/AMR15C">problem</a> ?↵
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**Reduced Problem Statement**↵
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Given $2$ integers $N$ and $K$. We are asked to print the lexographically smallest permutation of first $N$ natural number such that $abs(i - pos_i) \ge K$ for every $i \in [1, N]$ if it exists where $pos_i$ is the position of $i^{th}$ element in the permutation.↵
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**Constraints:**↵
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$1 \le N \le 10^5$ ↵
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$0 \le K \le N-1$↵
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**Example**↵
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**Input:**↵
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3↵
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2 2↵
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3 0↵
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3 1↵
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**Output:**↵
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-1↵
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1 2 3↵
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2 3 1↵
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**Explanation**↵
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For the first test case, N = 2 and K = 2. It is impossible to permute [1, 2] in any way such that abs(P[1]-1) >= 2 and abs(P[2]-2) >= 2. Hence, output is -1.↵
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For the second test case, N = 3 and K = 0. We can just set P[i] = i, and hence the answer is 1 2 3↵
For the third case, the valid permutations are [2, 3, 1] and [3, 1, 2]. The answer is [2, 3, 1] since it is lexicographically smaller than [3, 1, 2].
↵
Can anybody help me with the following <a href="https://www.codechef.com/ACMAMR15/problems/AMR15C">problem</a> ?↵
↵
**Reduced Problem Statement**↵
↵
Given $2$ integers $N$ and $K$. We are asked to print the lexographically smallest permutation of first $N$ natural number such that $abs(i - pos_i) \ge K$ for every $i \in [1, N]$ if it exists where $pos_i$ is the position of $i^{th}$ element in the permutation.↵
↵
**Constraints:**↵
↵
$1 \le N \le 10^5$ ↵
↵
$0 \le K \le N-1$↵
↵
**Example**↵
↵
**Input:**↵
↵
3↵
↵
2 2↵
↵
3 0↵
↵
3 1↵
↵
**Output:**↵
↵
-1↵
↵
1 2 3↵
↵
2 3 1↵
↵
**Explanation**↵
↵
For the first test case, N = 2 and K = 2. It is impossible to permute [1, 2] in any way such that abs(P[1]-1) >= 2 and abs(P[2]-2) >= 2. Hence, output is -1.↵
↵
For the second test case, N = 3 and K = 0. We can just set P[i] = i, and hence the answer is 1 2 3↵
For the third case, the valid permutations are [2, 3, 1] and [3, 1, 2]. The answer is [2, 3, 1] since it is lexicographically smaller than [3, 1, 2].
