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 sys import stdin, stdout
import math
import string

a, b, c = map(int, stdin.readline().split())
s = set()
counter = 0

while(True):
    counter+=1
    a*=10
    while(a<b):
        a*=10
        if c == 0:
            print(counter)
            exit()
        counter+=1

    x = a / b
    a = a % b
    if x == c:
        print(counter)
        break
    if a == 0 and c == 0:
        print(counter+1)
        break
    if a == 0:
        print(-1)
        break
    if a in s:
        print(-1)
        break
    else:
        s.add(a)
