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 = 10000
n,m,q = map(int,raw_input().split())
t = str(Decimal(n)/Decimal(m)) + '0'
dec = False
found = False
for j,i in enumerate(t):
    if j >= 10000:
        break
    if i == '.':
        point = j
        dec = True
    if dec== True and i == str(q):
        print j - point
        found = True
        break
if found == False:
    print -1

