You are given three integers a, b and . 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 positions i (1≤i<n) such that si≠si+1. It is guaranteed that the answer always exists.
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: