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Given an integer \$N\$ consider a permutation \$p=p_1,p_2,p_3,\ldots\$ of \$1,\ldots,N-1\$. Let \$P = p_1 , p_1+p_2 \bmod N, p_1+p_2+p_3 \bmod N, \ldots\$ be its prefix sums modulo \$N\$. Sometimes \$P\$ will be a permutation of \$1,\ldots,N-1\$ itself.
For example, \$N=4: p=3,2,1 \rightarrow P=3...