Description

Little Y finds there is a very interesting formula in mathematics:

X^Y mod Z = K

Given X, Y, Z, we all know how to figure out K fast. However, given X, Z, K, could you figure out Y fast?

Input

Input data consists of no more than 20 test cases. For each test case, there would be only one line containing 3 integers

X

,

Z

,

K

(0 ≤

X

,

Z

,

K

≤ 10

⁹

).

Input file ends with 3 zeros separated by spaces.

Output

For each test case output one line. Write "No Solution" (without quotes) if you cannot find a feasible

Y

(0 ≤

Y

<

Z

). Otherwise output the minimum

Y

you find.

5 58 33
2 4 3
0 0 0

9
No Solution

Source

POJ Monthly--2007.07.08

, Guo, Huayang