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. 
from decimal import *
a,b,c=map(int,input().split())
# print(a/b)
def f(z,c):
    
    l=(len(z))
 
    for i in range(1,l):
        if(z[i]==c):
            print(i)
            return
if c==0:
    z=str(a/b)[1:]
    getcontext().prec = 600
    zz=str(Decimal(a) / Decimal(b))[1:]
    # print(zz)
    # print(zz)
    # print(zz)
    # print(len(set(z)))
    if '0' in zz:
        f(zz,'0')
    elif len(zz)<500:
        print(len(z))
    else:
        print(-1)

    exit()
# print(a/b)
getcontext().prec = 600
z=str(Decimal(a) / Decimal(b))
# print(z)
c=str(c)

# print((z))
# if 'e' in z:
#     oo=z.index('e')
#     o=(z[:oo])
#     p=int(z[oo+2:])
#     if c in o:
#         print(o.index(c)+p)
#     else:
#         print(-1)
#     exit()

if a%b:
    # print('a')
    z=(str(z)[1:600])
    # print(z[590:])
    # print(z)
    # print(z)
    if c in z:
        # print(z.index((c)))
        f(z,c)
    # elif (c=='0'):
    #     print(len(z))
    else:
        print(-1)
else:
    if c==0:
        print(1)
    else:
        print(-1)