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. 
import decimal
decimal.setcontext(decimal.Context(prec=501))
#val = decimal.Decimal(1.0) / decimal.Decimal(7.0)
#print (val)
a,b,c = map(int, input().split())
i = 0
val = decimal.Decimal(a) / decimal.Decimal(b)
#print (val)
#print (i)
#print (c)
for i in range(1,501):
    val = val * 10
    #print (int(val % 10))
    if int(val % 10) == c:
        print (i)
        break
if i == 500:
    print ("-1")
    