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())



cntZeroes = 0
tenPw = 1

for i in range(1, 1000):
    tenPw *= 10
    if 1 * b <= a * tenPw:
        break
    cntZeroes += 1



for i in range(1000):
    a = a * 10
a //= b


if c == 0:
    if cntZeroes > 0:
        print(1)
        exit(0)

arr = []
while a > 0:
    arr.append(a%10)
    a //= 10

arr.reverse()
for i in range(len(arr)):
    if arr[i] == c:
        print(cntZeroes + i + 1)
        exit(0)
print(-1)
