You are given an irreducible fraction, ~\frac ab~. Let the initial value of a variable ~x~ be ~-1~. There are three available operations on ~x~:

1. + - Add ~-1~ to ~x~.
2. * - Multiply ~x~ by ~-1~.
3. ^ - Raise ~x~ to the power of ~-1~.

Note that ~x~ must be nonzero for operation type 3 ^.

Output any minimum length sequence of operations which makes ~x~ equal to ~\frac ab~. If it is not possible, output -1 instead.

Constraints

~|a| \le 10^6~
~1 \le b \le 10^6~

~\gcd(a,b) = 1~

Input Specification

The first line contains two space-separated integers, ~a~ and ~b~.

Output Specification

If there does not exist a sequence of operations which makes ~x~ equal to ~\frac ab~, output -1 on one line.

Otherwise, on the first line, output the minimum length of a valid operation sequence. On the second line, output a string consisting only of the characters +, *, and ^, describing any minimum length sequence of operations which makes ~x~ equal to ~\frac ab~.

Sample Input

2 3

Sample Output

5
+^+^*

Explanation for Sample

The values which ~x~ takes on during this sequence of operations are as follows:

~-1 \rightarrow -2 \rightarrow -\frac12 \rightarrow -\frac32 \rightarrow -\frac23 \rightarrow \frac23~

Note that +^+*^ would also be an acceptable operation sequence.

It can be shown that the minimal number of operations to transform ~x~ from ~-1~ to ~\frac23~ is ~5~.