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. 
import math
from decimal import *
getcontext().prec = 400
#print(Decimal(1) / Decimal(7))
(a,b,c) = [int(x) for x in input().split(' ')]
d=Decimal(a)/Decimal(b)
ans=-1
#print(d)
for i in range (1,300):
    d=10*d
    #print(d)
    last=int(d)
    d=d-last
    if last == c:
        ans = i
        print(ans)
        break
    
    
    
if ans == -1:
    print(ans)