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(" "))

a = a%b
i = 1
while i <= b :
    if a==0:
        if c==0 :
            print(i)
            exit()
        else :
            print(-1)
            exit()
    if a<b : a *= 10

    while(a<b) :
        if c==0 :
            print(i)
            exit()
        a *= 10
        i += 1
    d = a//b
    if d==c:
        print(i)
        exit()
    a -= d*b

    i += 1
print(-1)

