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. 
import sys, heapq

a,b,x = map(int, sys.stdin.readline().split())
temp = [1] * (x + 1)
for i in range(1, len(temp), 2):
    temp[i] = 0
ca = 0
cb = 0
for i in range(len(temp)):
    if temp[i]:
        cb += 1
    else:
        ca += 1
if a - ca < 0 or b - cb < 0:
    temp = [0] * (x + 1)
    for i in range(1, len(temp), 2):
        temp[i] = 1
    ca = 0
    cb = 0
    for i in range(len(temp)):
        if temp[i]:
            cb += 1
        else:
            ca += 1
    a -= ca
    b -= cb
    if len(temp) % 2 == 0:
        temp = [0] * a + temp + [1] * b
    else:
        temp = [0] * a + temp[:-1] + [1] * b + [0]
    print(''.join(map(str, temp)))
else:
    a -= ca
    b -= cb
    if len(temp) % 2 == 0:
        temp = [1] * b + temp + [0] * a
    else:
        temp = [1] * b + temp[:-1] + [0] * a + [1]
    print(''.join(map(str, temp)))