You are given three integers a, b and x. Your task is to construct a binary string s of length n = a + b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1 ≤ i < n) such that s_i ≠ s_{i + 1}. It is guaranteed that the answer always exists.

For example, for the string "01010" there are four indices i such that 1 ≤ i < n and s_i ≠ s_{i + 1} (i = 1, 2, 3, 4). For the string "111001" there are two such indices i (i = 3, 5).

Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.

Input

The first line of the input contains three integers a, b and x (1 ≤ a, b ≤ 100, 1 ≤ x < a + b).

Output

Print only one string s, where s is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.

Examples

Input

2 2 1


Output

1100


Input

3 3 3


Output

101100


Input

5 3 6


Output

01010100

Note

All possible answers for the first example: 

  * 1100; 
  * 0011. 



All possible answers for the second example: 

  * 110100; 
  * 101100; 
  * 110010; 
  * 100110; 
  * 011001; 
  * 001101; 
  * 010011; 
  * 001011. 
a,b,x=list(map(int,input().split()))
digit='0'
ans=""
kitne=a+b
l=[0 for j in range(kitne)]
k=0
while(x>1):
	if(k==(0//2)):
		if(not(a<b)):
			l[k]=0
			a-=1
		else:
			l[k]=1
			b-=1
	else:
		l[k]=abs(l[k-1]-1)
		if(l[k]!=0):
			b-=1
		else:
			a-=1
		x-=1
	k=k+(2//2)

if(l[k-1]!=0):
	while(not(b<=0)):
		l[k]=1
		k+=1
		b-=1
	while(not(a<=0)):
		l[k]=0
		k+=1
		a-=1
else:
	while(not(a<=0)):
		l[k]=0
		k+=1
		a-=1
	while(not(b<=0)):
		l[k]=1
		k+=1
		b-=1

for m in range(kitne):
	print(l[m],end="")
print()