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. 
#540_B

import decimal

ln = [int(i) for i in input().split(" ")]
a = ln[0]
b = ln[1]
c = ln[2]

oc = -1

for i in range(0, b + 5):
    q = (a * 10) // b
    a = (a * 10) % b
    if q == c:
        oc = i + 1
        break

print(oc)
