construct/rlve prefix product permutation
construct/rlve prefix product permutation: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find a permutation p 1, ..., p 109 of the integers 1, 2, ..., 109 such that the 109 prefix products p 1, p 1 p 2, ..., p 1 p 2 ... p 109 are pairwise distinct modulo 109.
The task
Find a permutation p_1, ..., p_109 of the integers 1, 2, ..., 109 such that the 109 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_109 are pairwise distinct modulo 109.