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 sys
def input():    return sys.stdin.readline().strip()
def iinput():   return int(input())
def minput():   return map(int, input().split()) 
def listinput(): return list(map(int, input().split()))
a,b,pos=minput()
for i in range(b):
	a*=10
	c=a//b
	a=a%b
	if c==pos:
		print(i+1)
		exit()
print("-1")