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. 
a,b,c = map(int,input().split())
res = ""
vara = [0 for i in range(1000001)]
while True:
    cnt = 0
    while a < b:
        a = a * 10
        cnt += 1
        if cnt > 1:
            res += "0"
    vara[a] += 1
    if vara[a] == 2:
        break
    res += str(a//b)
    a = a % b
    if a == 0:
        res += "0"
        break
c = str(c)
for i in range(len(res)):
    if c == res[i]:
        print(i+1)
        break
else:
    print(-1)