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 = list(map(int, input().split()))
a = A[0]
b = A[1]
c = A[2]
# get the mod of the number
a = a % b

index = 0
# traverse for every decimal places
for i in range(1, b + 1):

    # convert to the decimal places

    a = a * 10

    # condition we are checking is (a*10/b)/c
    if int(a / b) == c:
        index = i
        break

    # mod the number again
    a = a % b

# if we actually found an index
if index != 0:
    print(index)
else:
    print(-1)
		 	 	   			       	 			 			 		