Fractions

In a distant galaxy, long ago, people had not yet discovered positional numeral systems or natural fractions. To express numbers between 0 and 1, they used a method of decomposing them into a sum of reciprocals of natural numbers. Each fraction was represented as a sum where the denominators were distinct: q_i ≠ q_j for i ≠ j.

Given a natural fraction, your task is to find its decomposition according to the system used by the inhabitants of this distant galaxy.

Input

The input consists of two integers p and q such that 0 < p < q < 100. Each integer is provided on a separate line, with no spaces at the beginning or end of the line.

Output

Output the sequence of the required natural numbers q_1, ..., q_n in ascending order. Each number should be printed on a separate line, without spaces at the beginning or end of the line. The total number of these numbers should not exceed 239, and each number must be less than 10^9.