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 *

a, b, c = input().strip().split()

getcontext().prec = 10000

result = str(Decimal(int(a))/Decimal(int(b)))
result += "0"

dec = result.find(".")
ans = -1

for i in range(dec+1, min(10000,len(result))):
    if (result[i] == c):
        ans = i-dec
        break
    
print(ans)