PKU 2649: Factovisors

Factovisors
Time Limit: 1000MS　　Memory Limit: 65536K
Total Submissions: 1620　　　Accepted: 431

Description

The factorial function, n! is defined thus for n a non-negative ingeger:

　　　0! = 1
　　　n! = n * (n-1)!　　(n > 0)


We say that a divides b if there exists an integer k such that

　　　k*a = b



Input

The input to your program consists of several lines, each containing two non-negative integers, n and m, both less than 2^31.

Output

For each input line, output a line stating whether or not m divides n!, in the format shown below.

Sample Input

6 9
6 27
20 10000
20 100000
1000 1009

Sample Output

9 divides 6!
27 does not divide 6!
10000 divides 20!
100000 does not divide 20!
1009 does not divide 1000!

Source

Waterloo local 1999.01.31