Friendly Brothers

Time limit2sMemory limit128 MB

Summary

Given a reduced fraction a/b, find the shortest repeating turn pattern (length at most 60) of two people eating half the remaining cake so one person's total share equals a/b.

Level: Medium6 of 10
Topics: Number theory, Math, Bit manipulation, Brute force
Solved: No attempts yet

Problem

Youngsik and Minsik are sharing a cake. Whenever someone takes a turn, that person eats exactly half of the cake that remains.

If they alternate in the order Youngsik, Minsik, Youngsik eats the following amounts.

Youngsik	Minsik
1/2	1/4
1/8	1/16
1/32	1/64
1/128	1/256
...	...

In this case, Youngsik eats 2/3 of the whole cake, and Minsik eats 1/3.

Now the two brothers will repeat a fixed pattern forever. Each character of the pattern represents one turn; after the last character, the pattern starts again from the beginning. Youngsik is written as *, and Minsik is written as -.

For the repeated pattern Youngsik, Minsik, Youngsik, the amounts are taken as follows.

Youngsik	Minsik	Youngsik
1/2	1/4	1/8
1/16	1/32	1/64
1/128	1/256	1/512
...	...	...

With this pattern, Youngsik eats 5/7 of the whole cake.

You are given the target amount of cake Youngsik must eat as a reduced fraction a/b. Find the shortest repeating pattern that makes Youngsik eat exactly that amount.

Input

The first line contains two integers a and b. They are the numerator and denominator of the reduced fraction a/b.

Output

Print the eating pattern on the first line. In the pattern, print Youngsik's turns as * and Minsik's turns as -.

If no pattern of length at most 60 exists, print -1. If multiple patterns are possible, print the shortest one.

Constraints

0 <= a <= b <= 2^63 - 1
a and b are relatively prime.

Examples6

Example 1
Input
```
2 3
```
Expected output
```
*-
```
Example 2
Input
```
5 7
```
Expected output
```
*-*
```
Example 3
Input
```
0 1
```
Expected output
```
-
```
Example 4
Input
```
5 9
```
Expected output
```
*---**
```
Example 5
Input
```
1 2
```
Expected output
```
-1
```

Example 6

Input

76861433640456464 76861433640456465

Expected output

********************************************************----