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24/09/2023 21:15:18

# Рабочее место участника

## Задачи

1914. Sequence

Ограничения: время – 500ms/1000ms, память – 32MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод Послать решение Blockly Посылки Темы Где Обсудить (0)

Let's take any natural number K and generate an infinite sequence S according to the following rules.
• S_i is i, where 1\ ≤\ i\ ≤\ K.
• S_i is the least natural number so, that gcd(S_i,\ S_{i-1})\ ≥\ K and S_i\ ≠\ S_j, where 1\ ≤\ j\ <\ i and i\ >\ K and gcd mean "greatest common divisor".
For example, for K=3 first twenty terms are 1, 2, 3, 6, 9, 12, 4, 8, 16, 20, 5, 10, 15, 18, 21, 7, 14, 28, 24, 27.
Sooner or later in this sequence there will be all natural numbers. Write the program, which calculates the least natural number that is missing among first N terms, the greatest number among first N terms, and N-th term.
Input
The first line of the input file contains two integers K and N (1\ ≤\ K\ ≤\ 100, 1\ ≤\ N\ ≤\ 10000), separated by one space. First N terms of the sequence S do not exceed 30000 for given K.
Output
Write into the output file the one line containing three integers, separated by spaces. They are the least natural number that is missing among first N terms of the sequence S, the greatest number among first N terms of the sequence, and N-th term.

Sample Input

3 20


Sample Output

11 28 27 