Lexicographical Tuples Generation

Given two integers \(n\) and \(k\), generate all \(n\)-tuples where each element is an integer in the range \([1, k]\). The \(n\)-tuples must be printed in lexicographical order. For example, a tuple is defined as a sequence of \(n\) elements, e.g., \((1,1,2)\) is a 3-tuple and \((233,254,277,123)\) is a 4-tuple.

Lexicographical order means that tuples are ordered primarily by the first element, then by the second, and so on. For instance, when \(n=2\) and \(k=2\), the valid tuples in lexicographical order are:

1 1
1 2
2 1
2 2

Write a program to output all such \(n\)-tuples.

inputFormat

The input consists of two space-separated integers:

• \(n\): the length of each tuple
• \(k\): the maximum value for each element (each element is in \([1, k]\))

outputFormat

Output all \(n\)-tuples in lexicographical order. Each tuple should be printed on a separate line with its elements separated by a single space.

sample

1 3

1
2
3