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 *
import math
getcontext().prec=100000
a,b,c = map(int,input().split())
f = str(Decimal(a)/Decimal(b))
if len(f)<100000: f = f + '0'
suc = False
for i in range(2,10**5):
    if i == len(f): break
    if f[i] == str(c):
        print(i-1)
        suc = True
        break
if not suc: print(-1)
