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. 
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Date    : 2018-03-03 19:17:22
# @Author  : Lweleth (SoungEarlf@gmail.com)
# @Link    : https://github.com/
# @Version : $Id$

a, b, n = list(map(int, input().split()))
if a % b == 0 and n == 0:
	print(1)
	exit(0)
a %= b
ans = -1
for i in range(0, 1000):
	a *= 10
	if int(a / b) % 10 == n:
		ans = i + 1
		break
	if a > b:
		a -= int(a/b) * b
print(ans)