Contest Duration: - (local time) (100 minutes) Back to Home
C - Monotonically Increasing /

Time Limit: 2 sec / Memory Limit: 1024 MB

注記

ある 2 個の異なる長さの等しい整数列 A_1,A_2,\dots,A_NB_1,B_2,\dots,B_N が以下を満たすとき、またその時に限り辞書順で AB より早いと定義されます。

• ある整数 i(1 \le i \le N) が存在し、1 \le j < i である全ての整数 j に対し A_j=B_j が成り立ち、かつ A_i < B_i が成り立つ。

ある整数列 A_1,A_2,\dots,A_N は以下を満たすとき、またその時に限り狭義単調増加です。

• 全ての整数 i(1 \le i \le N-1) に対し A_i < A_{i+1} が成り立つ。

制約

• 1 \le N \le M \le 10
• 入力は全て整数。

入力

N M


入力例 1

2 3


出力例 1

1 2
1 3
2 3


入力例 2

3 5


出力例 2

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


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).

Sample Input 1

2 3


Sample Output 1

1 2
1 3
2 3


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

Sample Input 2

3 5


Sample Output 2

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