Numerology P50084

According to the Bible, 666 is the “number of the beast”. Indeed, in Revelation $\mit 13$:$\mit 18$ it is said:

“…count the number of the beast: for it is the
number of a man; and his number is 666.”

Many theologists have associated 666 with the Antichrist. Believe it or not, 666 has many interesting numerological properties. For instance, $$\begin{align*} 666 \enspace &= \enspace 3^6 - 2^6 + 1^6 \\ \enspace &= \enspace 1 + 2 + 3 + \cdots + 6 \cdot 6 \\ \enspace &= \enspace 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2 . \end{align*}$$

Another curious property is that it is possible (there are exactly two ways) to insert ‘+’ signs into the number 123456789 to get 666: $$666 \enspace = \enspace 1 + 2 + 3 + 4 + 567 + 89 \enspace = \enspace 123 + 456 + 78 + 9 ,$$ and it is also possible (there is exactly one way) to do the same with the number 987654321: $$666 \enspace = \enspace 9 + 87 + 6 + 543 + 21 .$$

Let’s play numerology. Write a program such that, given two numbers $n$ and $m$, prints all the ways to insert ‘+’ signs into $m$ so that the sum is $n$.

Input

Input consists of several cases. Every case has two strictly positive natural numbers $n$ and $m$, each not larger than $10^{12}$. Assume that the leftmost digit of $n$ and of $m$ is never zero.

Output

For every case, print all the ways to get $n$ by adding the digits of $m$ as explained above. The solutions must appear in lexicographical order. If no solution exists, state so.