Multisets (2) P70914

Statement

Write a program that, given three numbers $n$ , $x$ and $y$ , prints all the multisets that can be made up with $\{1, \dots, n\}$ , in such a way that every number appears between $x$ and $y$ times.

Input

Input consists of a natural number $n > 0$ , followed by a natural number $x \ge 0$ , followed by a natural number $y > x$ .

Output

Print all the multisets that can be made up with $\{1, \dots, n\}$ , using each number between $x$ and $y$ times. The numbers inside each multiset must appear in non-decreasing order.

Information about the checker

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

Public test cases

Input

2 1 4

Output

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

Information

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