Multisets (4) P14098

Statement

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Write a program that, given four natural numbers n, x, y and t, prints all the multisets with t ‍numbers that can be made up with {1, …, 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 ≥ 0, followed by a natural number y > x, followed by a natural number t ≥ 0. Assume nx ≤ t ≤ ny.

Output

Print all the multisets of size t that can be made up with {1, …, 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

3 1 4 6

Output

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

Information

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