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. 
ar = []
ar = input().split()
a = int(ar[0])
b = int(ar[1])
c = int(ar[2])
d = 1
for i in range(1000) :
    d *= 10
d = d * a
d = d // b
string = str(d)
while len(string) < 1000 :
    string = "0" + string
i = 0
for dig in map(int, string):
    i += 1
    if dig == c :
        break
if i == 1000 :
    print(-1)
else :
    print(i)