The product of *x* by *y* is stable
if the digits of *x* and *y* on one hand, and the
digits of *x* * *y* on the other hand, are the same ones.

For instance, the product

875 * 650 = 568750 |

is stable because in the both sides there is a 0, two 5, a 6, a 7 and a 8.

This property can be extended to other bases different of 10. For instance, the product of 3 by 53 is stable in base 2:

11 * 110101 = 10011111 |

because in both sides there are two 0 and six 1.

Your task is to write a program that, given a sequence of pairs *x* and *y*,
prints which bases between 2 and 16 (both included)
the product *x* * *y* is stable for.

To solve this problem, you must implement and use the function

that indicates if, in base *b* (2≤ *b*≤ 16),
*x* and *y* in one hand,
and *x* * *y* in the other one, have the same digits.

You must implement and use also the procedure

that prints *n* in base *b* in the screen
(just like that, without spaces nor line feeds).

**Input**

The input is a sequence of pairs of natural numbers *x* and *y*.
*x* ≥ 1, *y* ≥ 1, *x* * *and* ≤ 10^{9} are fulfilled.
You can assume this information
as a precondition of your procedures.

**Output**

For each pair *x* and *y*,
print which bases the product *x* * *y* is stable for.
If there is not any base, print it.
It must print a line feed after the output of each case.
Follow the format of the instance.

**Observation**

If you do tests with random numbers
and your program do not find any solution, do not worry:
most products are *not* stable.

Public test cases

**Input**

875 650 3 53 140 245 1 1 118 224

**Output**

solutions for 875 and 650 1101101011 * 1010001010 = 10001010110110101110 (base 2) 31223 * 22022 = 2022312232 (base 4) 4015 * 3002 = 20105034 (base 6) 875 * 650 = 568750 (base 10) solutions for 3 and 53 11 * 110101 = 10011111 (base 2) solutions for 140 and 245 10001100 * 11110101 = 1000010111111100 (base 2) 2030 * 3311 = 20113330 (base 4) 8C * F5 = 85FC (base 16) solutions for 1 and 1 none of them solutions for 118 and 224 A8 * 194 = 1894A (base 11)

Information

- Author
- Professorat de P1
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++