B. Binary String Constructing

B. Binary String Constructing

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given three integers aa, bb and xx. Your task is to construct a binary string ss of length n=a+bn=a+b such that there are exactly aa zeroes, exactly bb ones and exactly xx indices ii (where 1≤i<n1≤i<n) such that si≠si+1si≠si+1. It is guaranteed that the answer always exists.

For example, for the string "01010" there are four indices ii such that 1≤i<n1≤i<n and si≠si+1si≠si+1 (i=1,2,3,4i=1,2,3,4). For the string "111001" there are two such indices ii (i=3,5i=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 aa, bb and xx (1≤a,b≤100,1≤x<a+b)1≤a,b≤100,1≤x<a+b).

Output

Print only one string ss, where ss is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.

Examples

input

Copy

2 2 1

output

Copy

1100

input

Copy

3 3 3

output

Copy

101100

input

Copy

5 3 6

output

Copy

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

代码： 

#include <iostream>

using namespace std;

int main()
{
    int a,b,x;
    cin>>a>>b>>x;
    int flag;
    if(a>=b) flag=0;
    else flag=1;
    while(x!=1)
    {
        x--;
        if(flag){
            cout<<1;
            b--;
        }else{
            cout<<0;
            a--;
        }
        flag=1-flag;
    }
    if(flag==0){
        while(a!=0){
            cout<<0;
            a--;
        }
        while(b!=0)
        {
            cout<<1;
            b--;
        }
    }
    else{
        while(b!=0){
            cout<<1;
            b--;
        }
        while(a!=0){
            cout<<0;
            a--;
        }
    }
    cout<<endl;
    return 0;
}