The following languages are only available languages for the problems from the contest

VK Cup 2015 - Wild Card Round 1:

- Picat 0.9

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Sum and product

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given integers *N* and *D*. Find *N* positive integers *x*_{1}...*x*_{N} such that the difference of their product and their sum equals *D*.

Input

The only line of input contains integers *N* (2 ≤ *N* ≤ 1000) and *D* (0 ≤ *D* ≤ 1000).

Output

Output *N* integers that satisfy the given condition in non-decreasing order (in a single line, separated with spaces). Note that some numbers can be equal. Numbers printed by you must not exceed 10^{6}.

Examples

Input

2 1

Output

2 3

Input

3 5

Output

1 2 8

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/17/2019 22:42:48 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|