benchmarks/Algorithms/linear_modular_inverse/problem.md

P3811 — Multiplicative Inverses Modulo a Prime

Description

Given positive integers $n$ and $p$, find the multiplicative inverse modulo $p$ of every integer in $[1,n]$.

An integer $x$ is a multiplicative inverse of $a$ modulo $p$ if

$$ax\equiv 1(\mathrm{m}\mathrm{o}\mathrm{d}p)\mathrm{.}ax\; \backslash equiv\; 1\; \backslash pmod\; p.$$

The input guarantees that $p$ is prime.

Input

The only line contains two positive integers $n$ and $p$.

Output

Print $n$ lines. The $i$-th line contains the multiplicative inverse of $i$ modulo $p$.

Constraints

• $1 \le n \le 3\times10^6$.
• $n < p < 20000528$.
• $p$ is prime.

Source

Luogu P3811, "Multiplicative Inverses Modulo a Prime".