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. 
from sys import stdin
rr = lambda: stdin.readline().strip()
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())

debug=0
if debug:
    fi = open('t.txt','r')
    rr = lambda: fi.readline().replace('\n','')

def solve(A,B, target):
    A %= B
    pos = 1
    seen = set()
    while A not in seen:
        seen.add(A)
        r, A = divmod(10*A, B)
        if r == target: return pos
        pos += 1
        
    return -1

print solve(*rrm())
