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())

'''tmp = (str(a/b))[2:]
if len(tmp) < 15:
    tmp += '0'
a = ((tmp).find(str(c)) + 1)
if a == 0:
    print(-1)
else:
    print(a)'''

#period = ''
#a *=  10**5
copy = str(a) + '0' * 100000
div = []
#dig = []
i = 0
while True:
    if a == 0:
        if a == c:
            print(i)
            exit()
        break
    #a *= 10**(len(str(b)))
    #dig.append(int(str(a)[0:len(str(b))]) // b)
    if a // b == c and i != 0:
        print(i)
        exit()
    #print(a)
    a = int(str(a % b) + copy[i + len(str(b))])
    if a in div:
        if a == c:
            print(i)
            exit()
        break
    else:
        div.append(a)
    i += 1
    
print(-1)
    
    

    
    