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. 
zeros, ones, swaps = map(int, raw_input().strip().split(' '))

numSubstr = swaps + 1
numBigger = None
charBigger = None
numSmaller = None
charSmaller = None
if zeros > ones:
    numBigger = zeros
    charBigger = "0"
    numSmaller = ones
    charSmaller = "1"
else:
    numBigger = ones
    charBigger = "1"
    numSmaller = zeros
    charSmaller = "0"

numStrBigger = numSubstr / 2
numStrSmaller = numSubstr / 2
if numSubstr%2 == 1:
    numStrBigger += 1
origBigger = numStrBigger
origSmaller = numStrSmaller

charPerStrBigger = numBigger/numStrBigger
charPerStrSmaller = numSmaller/numStrSmaller

currentBigger = True
r = []
while numStrBigger > 0 or numStrSmaller > 0:
    if currentBigger:
        for i in xrange(charPerStrBigger):
            r.append(charBigger)
    else:
        for i in xrange(charPerStrSmaller):
            r.append(charSmaller)
    if currentBigger and numStrBigger == 1:
        for i in xrange(numBigger%origBigger):
            r.append(charBigger)
    if not currentBigger and numStrSmaller == 1:
        for i in xrange(numSmaller%origSmaller):
            r.append(charSmaller)
    if currentBigger:
        currentBigger = False
        numStrBigger -= 1
    else:
        currentBigger = True
        numStrSmaller -= 1
        
rAct = "".join(r)
print rAct