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 Decimal, getcontext
a, b, c = [int(k) for k in input().split(' ') if k]
getcontext().prec = 5000
v = str(Decimal(a) / b).split('.')
if b % 5 == 0 or b % 2 == 0 or b == 1:
    v[1] += '0'
try:
    s = v[1].index(str(c))
    if s == getcontext().prec - 1:
        print(-1)
    else:
        print(len(v[0]) + s)
except:
    print(-1)
