Inversions in Permutations

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**Note**: For the problem KPERM, we have observed that PYPY3 performs better than Python3. You are given integers $N$, $R$ and $K$. Consider all permutations of the integers $1$ through $N$ with exactly $R$ inversions. Find the $K$-th lexicographically smallest among these permutations. Notes: - The number of inversions in a permutation $P_1, P_2, \ldots, P_N$ is the number of pairs of inte

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