Binary String Constructing CodeForces - 1003B （构造）

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 $a$, $b$ 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 $1\le i<n$) such that $s_i\ne s_{i+1}$. It is guaranteed that the answer always exists.

For example, for the string "01010" there are four indices $i$ such that $1\le i<n$ and $s_i\ne s_{i+1}$ ($i=1,2,3,4$). 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 $x$ ($1\le a,b\le 100,1\le x<a+b)$.

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

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.

题意：给出a，b，x，构造一个01串，有a个0，b个1。这个01串刚好有x个 ai 使得ai！=ai+1。

思路：对于x，我们很容易就可以想到先输出x/2对0和1（n对0和1交错出现可以提供2*n-1个符合题意的ai），然后将剩余的0和剩余的1连续输出（提供1个符合条件的ai，这样就刚好是x个符合条件的ai了，需要注意的是，我们要优先将个数多的放在前面，例如，有10个1,5个0的话，我们先输出x/2个“10”，否则，输出x/2个“01”）。

#include "iostream"
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;
    }
    return 0;
}