Division

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Description

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.

Hint

None

Source

University of Waterloo Local Contest 2001.01.

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