LogiQuest

213. Combination Sum

MediumBacktracking

Using the distinct positive candidates (each usable any number of times), print every combination that sums to the target. Each combination is printed in non-decreasing order; combinations are printed in lexicographic order. Print NONE if there are none.

Input format

Line 1: n target Line 2: n distinct positive integers

Output format

One combination per line, or NONE.

Example 1

Input

4 7
2 3 6 7

Output

2 2 3
7

Example 2

Input

3 8
2 3 5

Output

2 2 2 2
2 3 3
3 5

Constraints

1 ≤ n ≤ 10 1 ≤ target ≤ 40

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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