Self-Replicating Numbers

Time Limit: 10 Seconds Memory Limit: 32768 KB
Special Judge

Vasya's younger brother Misha is fond of playing with numbers. Two days ago he discovered that 9376² = 87909376 -- the last four digits constitute 9376 again. He called such numbers self-replicating. More precisely, an n-digit number is called self-replicating if it is equal to the number formed by the last n digits of its square. Now Misha often asks Vasya to help him to find new such numbers. To make the things worse Vasya's brother already knows what the scales of notation are, so he asks Vasya to find, for example, hexadecimal or binary self-replicating numbers.

Vasya wants to help his brother, but unfortunately he is very busy now: he is seriously preparing and training for the next ACM Regional Contest. So he asked you to write a program that for a given base b and length n will find all n-digit self-replicating numbers in the scale of notation with base b.

Input

Input consists of multiple test cases.
Each case occupies one line which contains two numbers b and n separated by a single space, the base b of the scale of notation (2

36) and required length n (1

2000).

Output

For each test case, print in the first line an integer K -- the total number of self-replicating numbers of length n in base b. Next K lines contain one n-digit number in base b each. Uppercase Latin characters from A to Z must be used to represent digits from 10 to 35 when b > 10. The self-replicating numbers can be listed in arbitrary order.

Sample Input

10 4
12 6

Sample Output

Submit

Source: Northeastern Europe 2002, Northern Subregion