Problem Description

Search is important in the acm algorithm. When you want to solve a problem by using the search method, try to cut is very important.
Now give you a number sequence, include n (<=1000) integers, each integer not bigger than 2^31, you want to find the first P subsequences that is not decrease (if total subsequence W is smaller than P, than just give the first W subsequences). The order of subsequences is that: first order the length of the subsequence. Second order the sequence of each integer’s position in the initial sequence. For example initial sequence 1 3 2 the total legal subsequences is 5. According to order is {1}; {3}; {2}; {1,3}; {1,2}. {1,3} is first than {1,2} because the sequence of each integer’s position in the initial sequence are {1,2} and {1,3}. {1,2} is smaller than {1,3}. If you also can not understand , please see the sample carefully.

Input

The input contains multiple test cases.
Each test case include, first two integers n, P. (1<n<=1000, 1<p<=10000).

Output

For each test case output the sequences according to the problem description. And at the end of each case follow a empty line.

3 5
1 3 2
3 6
1 3 2
4 100
1 2 3 2

1
3
2
1 3
1 2

1
3
2
1 3
1 2

1
2
3
1 2
1 3
2 3
2 2
1 2 3
1 2 2

Hint

Hint : You must make sure each subsequence in the subsequences is unique.

Author

yifenfei