Given t, a, b positive integers not bigger than 2147483647, establish whether (t^a - 1)/(t^b -1) is an integer with less than 100 digits.

Input

Each line of input contains t, a, b.

Output

For each line of input print the formula followed by its value, or followed by "is not an integer with less than 100 digits.", whichever is appropriate.

Sample Input

2 9 3
2 3 2
21 42 7
123 911 1

Sample Output

(2^9-1)/(2^3-1) 73
(2^3-1)/(2^2-1) is not an integer with less than 100 digits.
(21^42-1)/(21^7-1) 18952884496956715554550978627384117011154680106
(123^911-1)/(123^1-1) is not an integer with less than 100 digits.

Source

Waterloo local 2001.01.27