900_B. Position in Fraction
You have a fraction <image>. You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.

Input

The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).

Output

Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.

Examples

Input

1 2 0


Output

2

Input

2 3 7


Output

-1

Note

The fraction in the first example has the following decimal notation: <image>. The first zero stands on second position.

The fraction in the second example has the following decimal notation: <image>. There is no digit 7 in decimal notation of the fraction. 
```python
a,b,c = map(int, input().split())
t = a
q, r = divmod(t, b)
for i in  range(1, 10**5+1):
    q, r = divmod(r*10, b)
    #print(q)
    if q == c:
        print(i)
        exit()
else:
    print(-1)

```