Write a program that, given two numbers n and x, prints all the multisets that can be made up with {1, …, n}, in such a way that every number appears at most x times.

Input

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

Output

Print all the multisets that can be made with {1, …, n}, using each number at most x times. 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**

2 3

**Output**

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

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++ Python