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. 
#https://codeforces.com/contest/1003/problem/B

a,b,x = map(int,input().split())
n1 = x%2
n2 = x//2

if n1==1 and a>=b:
    print("01"*n2 + "0"*(a-n2) + "1"*(b-n2))
elif n1==1 and a<b:
    print("10"*n2 + "1"*(b-n2) + "0"*(a-n2))
elif n1==0 and a>=b:
    print("01"*(n2) + "1"*(b-n2) + "0"*(a-n2))
elif n1==0 and a<b:
    print("10"*(n2) + "0"*(a-n2) + "1"*(b-n2))         



# while i < n:
#     if a>0:
#         if y!=0 and a>1:
#             s.append("00")
#             i+=2
#             y-=1
#             a-=2

#         else:
#             s.append("0")
#             i+=1
#             a-=1

#     if b>0:
#         if i<n:
#             if y!=0 and b>1:
#                 s.append("11")
#                 i+=2
#                 y-=1
#                 b-=2
#             else:
#                 s.append("1")
#                 i+=1
#                 b-=1
    

# s = "".join(s)
# print(s)

# if a>1 and b>1 and x>1:
#     s.append("01")
# elif a>1:
#     s.append("0")
# elif b>1:
#     s.append("1")