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. 
string = raw_input()
al,bl,x = string.split()
al = int(al)
bl = int(bl)
x  = int(x)
ans = ''
if bl >= al:
    for a in range (0, x):
        if len(ans) <= x:
            ans += '1'
        else:
            break
        if len(ans) <= x:
            ans += '0'
        else:
            break
else:
    for a in range (0, x):
        if len(ans) <= x:
            ans += '0'
        else:
            break
        if len(ans) <= x:
            ans += '1'
        else:
            break
count0 = 0
count1 = 0
for a in ans:
    if a == '1':
        count1+=1
    if a =='0':
        count0+=1
add0 = al- count0
add1 = bl-count1
final = ''
beta = ''
eta = ''
if bl>=al:
    for a in range(0, add0):
        beta+= '0'
    for a in range (0, add1):
        eta += '1'
    final = ans[:1]+beta+ans[1:]
    ans = ''
    ans = eta+final
    print ans
else:
    for a in range(0, add1):
        beta+= '1'
    for a in range (0, add0):
        eta += '0'
    final = ans[:1]+beta+ans[1:]
    ans = ''
    ans = eta+final
    print ans