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. 
from decimal import *
getcontext().prec = 1000
a, b, c = map(int, input().split())
if a==b:
        if c == 0:
                print(1)
        else:
                print(-1)
        exit(0)
d = Decimal(a) / Decimal(b)
c = str(c)
s = str(d)
s = s.split('.')[1]
if len(s) > 999:
        s = s[:-1]
cnt = 1
for i in s:
        if(i==c):
                print(cnt)
                exit(0)
        cnt+=1
else:
        if(c == '0' and cnt != 1000):
                print(cnt)
        else:
                print(-1)
