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,raw_input().strip().split(' '))
yes = 0
a = a%b
d = {}
count = 0
k = 0
while(yes==0):
    # print a,b,
    if a in d:
        yes = 1
    d[a] = 1
    tcc = -1
    while(a<b and a!=0):
        a = a*10
        tcc+=1
    x = a/b
    # print x,count,a
    # print d
    a = a%b
    count+=1

    tc = 0
    pop = tcc*"0"+str(x)
    # print pop
    for i in pop:
        if i==str(c):
            k = 1
            print count+tc
            yes = 1
            break
        tc+=1
    if tcc!=-1:
        count+=tcc
if k==0:
    print -1
