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, k = input().split(' ')
a = int(a)
b = int(b)
# b = int(input())

cnt0 = 0
v = a / b
while (int(10 * v) == 0):
  v *= 10
  cnt0 += 1
# if int(10 * (a / b)) == 0:
#   print(1)
#   exit(0)

if k == '0' and cnt0 > 0:
  print(1)
  exit(0)

a *= int(10**100000)

a //= b

a = str(a)

# print(a)

l = len(a)
for i in range(l - 100):
  if a[i] == k:
    print(i + 1 + cnt0)
    exit(0)

print(-1)