Problems
Given the number of times N that a die is rolled and the output format type, write a program that outputs results according to the value of type as follows.
type = 1 : Print all possible outcomes when rolling a die N times.
type = 2 : Print all possible outcomes when rolling a die N times, excluding duplicate cases.
type = 3 : Print all possible outcomes when rolling a die N times where all numbers are different.
Examples of duplicates
1 1 2 is considered a duplicate of: 1 2 1, 2 1 1
1 2 3 is considered a duplicate of: 1 3 2, 2 1 3, 2 3 1, 3 1 2
Input
The first line contains the number of die rolls N (2 ≤ N ≤ 5) and the output format type (1 ≤ type ≤ 3).
Output
Output the cases for rolling a die N times according to the specified type. Print in order starting from smaller numbers.
Example #1
3 1
1 1 1
1 1 2
1 1 3
1 1 4
1 1 5
1 1 6
1 2 1
…
6 6 6
Example #2
3 2
1 1 1
1 1 2
…
1 1 6
1 2 2
…
5 6 6
6 6 6
Example #3
3 3
1 2 3
1 2 4
1 2 5
1 2 6
1 3 2
1 3 4
…
6 5 3
6 5 4
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