- Prepare
- Data Structures
- Trees
- Square-Ten Tree

# Square-Ten Tree

# Square-Ten Tree

The square-ten tree decomposition of an array is defined as follows:

- The lowest () level of the square-ten tree consists of single array elements in their natural order.
- The level (starting from ) of the square-ten tree consists of subsequent array subsegments of length in their natural order. Thus, the level contains subsegments of length , the level contains subsegments of length , the level contains subsegments of length , etc.

In other words, every level (for every ) of square-ten tree consists of array subsegments indexed as:

The image below depicts the bottom-left corner (i.e., the first array elements) of the table representing a square-ten tree. The levels are numbered from bottom to top:

**Task**

Given the borders of array subsegment , find its decomposition into a minimal number of nodes of a square-ten tree. In other words, you must find a subsegment sequence such as for every , , , where every belongs to any of the square-ten tree levels and is minimal amongst all such variants.

**Input Format**

The first line contains a single integer denoting .

The second line contains a single integer denoting .

**Constraints**

- The numbers in input do not contain leading zeroes.

**Output Format**

As soon as array indices are too large, you should find a sequence of square-ten tree level numbers, , meaning that subsegment belongs to the level of the square-ten tree.

Print this sequence in the following compressed format:

- On the first line, print the value of (i.e., the compressed sequence block count).
- For each of the subsequent lines, print space-separated integers, and (, ), meaning that the number appears consequently times in sequence . Blocks should be listed in the order they appear in the sequence. In other words, should be equal to , should be equal to , etc.

Thus must be true and must be true for every . All numbers should be printed without leading zeroes.

**Sample Input 0**

```
1
10
```

**Sample Output 0**

```
1
1 1
```

**Explanation 0**

Segment belongs to level of the square-ten tree.