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 = raw_input().split()
a=int(a)
b=int(b)
ce=int(c)
op=a/float(b)

a=a*(10**100010)
z=a/b
k=str(z)
plus=0
ans=-1
u=0
if op<0.1 :
	u+=1
if op<0.01 :
	u+=1
if op<0.001 :
	u+=1
if op<0.0001 :
	u+=1
if op<0.00001 :
	u+=1
if op<0.000001 :
	u+=1
if op<0.1 and ce==0 :
	print(1)

else:
 while(plus<=100000):
	if(k[plus]==c):
		ans=plus+1+u
		break;
	
	plus+=1
	

 print(ans)