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. 
###modular exponentiation: a^n % M
#pow(a, n, M) 
### gcd: gcd(a, b)
#import fractions
#fractions.gcd(a, b)
### LCM (M, N)
#lcm = M*N/fractions.gcd(M, N)

def get_res(a, b, c):
    #while a/b == 0:
    #    a *= 10
    N = 100000
    #print a, b
    a *= 10
    for i in range(N):
        q = a / b
        r = a % b
        a = (a - q*b)*10
        if q == c:
            return i+1
    return -1

a, b, c = [int(s) for s in raw_input().split(" ")]
result = get_res(a, b, c)
print "{}".format(result)
