Because of necessary software maintenance, Jutge.org may not work well on the afternoons of the 20th and 21th of april.

Multisets (3) P22110

Statement

html

Write a program that, given two numbers n and t, prints all the multisets with t numbers that can be made up with {1, …, n}.

Input

Input consists of a natural number n > 0, followed by a natural number t ≥ 0.

Output

Print all the multisets of size t that can be made up with {1, …, n}. The numbers inside each multiset must appear in non-decreasing order.

You can print the solutions to this exercise in any order.

Public test cases

Input

3 3

Output

{3,3,3}
{2,3,3}
{2,2,3}
{2,2,2}
{1,3,3}
{1,2,3}
{1,2,2}
{1,1,3}
{1,1,2}
{1,1,1}

Information