Find all nondecreasing sequences of positive numbers which sum to a given number.

### Input

In the first line there will be a number of data sets *t*. In the next t lines data sets follows. Each data set is a single number *n _{i}*.

### Output

For each data set write all nondecreasing sequences of positive numbers which sum to *n _{i}*. Sequences should be ordered in a lexicographical order and separated by new lines.

### Example

Input:2 1 5Output:1 1 1 1 1 1 1 1 1 2 1 1 3 1 2 2 1 4 2 3 5