Goal
A polydivisible number (or magic number) is a number with digits abcde... that has the following properties :
- Its first digit a is not 0.
- The number formed by its first two digits ab is a multiple of 2.
- The number formed by its first three digits abc is a multiple of 3.
- The number formed by its first four digits abcd is a multiple of 4.
- etc...
For example, 567 is polydivisible because :
- 5 is divisible by 1
- 56 is divisible by 2
- 567 is divisible by 3
Your program will have to determine in which bases the input number may be, knowing that it is polydivisible in base 10
Input
One line containing the number consisting of pairs of numbers separated by spaces
01 02 03 => 123 in base 10
01 02 03 => 123 in base 16 => 291 in base 10
01 10 02 => 1A2 in base 16 => 418 in base 10
Output
The values of the bases by numeric order (one value <=> one line)
Constraints
2 ≤ base ≤36
number of digits < 18
Example
Output
5
6
8
9
11
12
14
15
16
20
24
28
29
35
