Permutations and cycles (1)

Write a program to print all the permutations of $\{1, \ldots, n\}$ with exactly $k$ cycles, where $1 \le k \le n$ . For exemple, consider the permutation $(4, 3, 2, 5, 1, 7, 6)$ . At position $1$ there is a $4$ , at position $4$ there is a $5$ , and at position $5$ there is a $1$ . Therefore, one of the cycles is $1 \rightarrow 4 \rightarrow 5 \rightarrow 1$ . The other two cycles are $2 \rightarrow 3 \rightarrow 2$ and $6 \rightarrow 7 \rightarrow 6$ . The permutation $(3,2,1)$ has the two cycles $1 \rightarrow 3 \rightarrow 1$ and $2 \rightarrow 2$ , and the permutation $(3,4,5,6,7,1,2)$ only has the cycle $1 \rightarrow 3 \rightarrow 5 \rightarrow 7 \rightarrow 2 \rightarrow 4 \rightarrow 6 \rightarrow 1$ .

Input

Input consists of $n$ and $k$ , with $1 \le k \le n$ .

Output

Print all the permutations of $\{1, \ldots, n\}$ with $k$ cycles.

Information about the checker

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

Hint

A possible program does not build the permutations consecutively from left to right, but jumping over the solution, using a function

    void f(int i, int ini, int cells, int cycles);

where @i@ is the next cell to fill, @ini@ is where the current cycle—still to be closed—starts, @cells@ is the number of cells still free, and @cycles@ is the number of cycles yet to be created.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T12:03:59.828Z