We call a positive integer $x$ a run number if all digits of $x$ are the same. For example, $4$, $111$, $888\,888$ are run numbers, while $27$, $334$, $100\,000$ are not.

Given an $n$-digit number $k$, represent $k$ as a sum of at most $(n + 1)$ run numbers. One can prove that a solution always exists.

Input

The first line contains an integer $t$, the number of test cases ($1 \le t \le 100$).

Each test case consists of one line containing two integers: $n$ and $k$ ($1 \le n \le 17$, $10^{n - 1} \le k < 10^n$).

Output

For each test case:

• On the first line, print an integer $m$: the number of run numbers which add up to $k$ ($1 \le m \le n + 1$).
• On the second line, print the $m$ run numbers in any order.
• If there are multiple solutions, print any one of them.

Examples

Input 1

2
4 2024
3 506

Output 1

4
999 999 22 4
3
444 55 7

Input 2

2
17 99999999999999999
9 333666999

Output 2

1
99999999999999999
3
333333333 333333 333