Doraemon's Number Game III

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Doraemon likes to play number game with Nobita.

One day, Doraemon came up with an idea, he gave a number *a* in base 10 and a number *x* (*x* < 10), and then he let Nobita multiplies the first digit of *a* with *x* and add the second digit of *a*, then multiplies *x* again and add the third digit of *a*. Do the above rules until there is only one digit (the leftmost digit of a is called the first digit).

For example, let *a* = 123, *x* = 2.
Then, 123 → (1*2+2)*2+3=11 → 1*2+1=3.
That is to say, Nobita should give the answer 3.

Sometimes *a* is too large, Nobita cannot work it out, can you help him?

#### Input

Input contains multiple cases, process to the end of file. Each case contains one line which contains only one number *a* (the length of *a* would not exceed 100000) as described above.

#### Output

For each case, you need to output the number when *x* = 1, 2 ... 9. You should output the nine numbers in one line separated by a single space.

#### Sample Input

123

#### Sample Output

6 3 4 9 8 7 9 9 9

Author:

**QU, Zhe**
Contest:

**ZOJ Monthly, December 2010**
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