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C - Monotonically Increasing

Score : $300$ points

Problem Statement

Print all strictly increasing integer sequences of length $N$ where all elements are between $1$ and $M$ (inclusive), in lexicographically ascending order.

Notes

For two integer sequences of the same length $A_1,A_2,\dots,A_N$ and $B_1,B_2,\dots,B_N$, $A$ is said to be lexicographically earlier than $B$ if and only if:

• there is an integer $i$ $(1 \le i \le N)$ such that $A_j=B_j$ for all integers $j$ satisfying $1 \le j < i$, and $A_i < B_i$.

An integer sequence $A_1,A_2,\dots,A_N$ is said to be strictly increasing if and only if:

• $A_i < A_{i+1}$ for all integers $i$ $(1 \le i \le N-1)$.

Constraints

• $1 \le N \le M \le 10$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the sought sequences in lexicographically ascending order, each in its own line (see Sample Outputs).

2 3

1 2 
1 3 
2 3 

The sought sequences are $(1,2),(1,3),(2,3)$, which should be printed in lexicographically ascending order.

3 5

1 2 3 
1 2 4 
1 2 5 
1 3 4 
1 3 5 
1 4 5 
2 3 4 
2 3 5 
2 4 5 
3 4 5