Distinct Investment Distribution

Nadan is a successful businessman who often invests in software developers. This year, he decided to distribute \(K\) kuna among \(N\) projects such that each project receives at least 1 kuna, and the amounts distributed to any two different projects are distinct positive integers.

It is guaranteed that a valid distribution exists.

inputFormat

The input consists of two space-separated integers \(N\) and \(K\), where \(N\) is the number of projects and \(K\) is the total kuna to distribute.

outputFormat

Output \(N\) space-separated positive integers representing the funds allocated to each project. These numbers must be distinct and their sum must equal \(K\).

sample

3 8

1 2 5