Sums of 1, 2, 3 (2)

There are 7 ways to write the integer 4 as a sum of 1, 2, and 3. Every sum uses at least one number.

• 1+1+1+1
• 1+1+2
• 1+2+1
• 2+1+1
• 2+2
• 1+3
• 3+1

Sorted in lexicographic order, they come out in this order.

1. 1+1+1+1
2. 1+1+2
3. 1+2+1
4. 1+3
5. 2+1+1
6. 2+2
7. 3+1

Given integers $n$ and $k$, write a program that finds the expression ranked $k$-th in lexicographic order among the ways to write $n$ as a sum of 1, 2, and 3.

The first line contains two integers $n$ and $k$ separated by a space. $n$ is a positive integer smaller than 11, and $k$ is a natural number at most $2^{31}-1$.

Print the expression ranked $k$-th in lexicographic order among the ways to write $n$ as a sum of 1, 2, and 3. Do not put spaces around the plus signs. If there is no $k$-th expression, print -1.