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. 
#!/usr/bin/env python3
# encoding: utf-8



#----------
# Constants
#----------



#----------
# Functions
#----------
def decision(a, b, x):
    x += 1
    assert a <= b
    s = 'B' * (x % 2) + 'AB' * (x // 2)
    a -= (x // 2)
    b -= (x // 2) + (x % 2)
    return s.replace('A', 'A'*(a+1), 1).replace('B', 'B'*(b+1), 1)


def calc(a, b, x):
    if a <= b:
        return decision(a, b, x).replace('A', '0').replace('B', '1')
    else:
        return decision(b, a, x).replace('A', '1').replace('B', '0')


# Reads a string from stdin, splits it by space chars, converts each
# substring to int, adds it to a list and returns the list as a result.
def get_ints():
    return [ int(n) for n in input().split() ]


# Reads a string from stdin, splits it by space chars, converts each substring
# to floating point number, adds it to a list and returns the list as a result.
def get_floats():
    return [ float(n) for n in input().split() ]


#----------
# Execution start point
#----------

if __name__ == "__main__":
    a = get_ints()
    assert len(a) == 3
    a, b, x = a[0], a[1], a[2]
    s = calc(a, b, x)
    print(s)
