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. 
"""
Task:
Given fraction a/b find the first occurence of
digit c in the decimal notation of the fraction
after the decminal point
"""

a, b, c = map(int, input().split())
q, r = divmod(a, b)
under = a - (b * q)

after_decimal_point = ''
for _ in range(b):
    under *= 10
    q, r = divmod(under, b)
    under -= b * q
    after_decimal_point += str(q)

location = after_decimal_point.find(str(c))
if location == -1:
    print(-1)
else:
    print(location + 1)