Binary String Constructing（cf）

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.

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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

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.                        

• 找规律.......

#include<bits/stdc++.h>
using namespace std;
int main()
{
    int a,b,x,n;
    char u,v;
    cin>>a>>b>>x;
    n=a+b;
    if(a>b)
        u='0',v='1';
    else
    {
        u='1',v='0';
        swap(a,b);
    }
    for(int i=0; i<x/2; i++)
    {
        cout<<u<<v;
        a--,b--;
    }
    if(x%2==0)
    {
        while(b--)
            cout<<v;
        while(a--)
            cout<<u;
    }
    else
    {
        while(a--)
            cout<<u;
        while(b--)
            cout<<v;
    }
}