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 java.util.*;
import java.io.*;
import java.math.*;
public class Mai5
{
    static class Reader 
    { 
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public Reader() { this(System.in); }public Reader(InputStream is) { mIs = is;} 
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];} 
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;} 
        public String s(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();} 
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;} 
        public int i(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;} 
        public double d() throws IOException {return Double.parseDouble(s()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
        public int[] arr(int n){int[] ret = new int[n];for (int i = 0; i < n; i++) {ret[i] = i();}return ret;}
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////
    //    RRRRRRRRR            AAA             HHH     HHH     IIIIIIIIIIIII   LLL           //
    //    RR    RRR           AAAAA            HHH     HHH      IIIIIIIIIII    LLL           //
    //    RR   RRR           AAAAAAA           HHH     HHH          III        LLL           //
    //    RR  RRR           AAA   AAA          HHHHHHHHHHH          III        LLL           //
    //    RRRRRR           AAA     AAA         HHHHHHHHHHH          III        LLL           //
    //    RR  RRR         AAAAAAAAAAAAA        HHH     HHH          III        LLL           //
    //    RR    RRR      AAA         AAA       HHH     HHH      IIIIIIIIIII    LLLLLLLLLLLL  //
    //    RR     RRR    AAA           AAA      HHH     HHH     IIIIIIIIIIIII   LLLLLLLLLLLL  //
    ///////////////////////////////////////////////////////////////////////////////////////////
    static int cache[][][][];
    static int x;
    public static int dp(int a,int b,int prev,int taken)
    {
        if(a==0&&b==0&&taken==x)
        return cache[a][b][prev][taken]=10000;
        if(a==0&&b==0&&taken!=x)
        return cache[a][b][prev][taken]=-10000;
        if(taken>x)
        return cache[a][b][prev][taken]=-10000;
        if(cache[a][b][prev][taken]!=-1)
        return cache[a][b][prev][taken];
        if(a>0&&b>0)
        {
            if(prev==0)
            return cache[a][b][prev][taken]=Math.max(dp(a-1,b,0,taken),dp(a,b-1,1,taken+1));
            else
            return cache[a][b][prev][taken]=Math.max(dp(a-1,b,0,taken+1),dp(a,b-1,1,taken));
        }
        else if(a==0)
        {
            if(prev==0)
            return cache[a][b][prev][taken]=dp(a,b-1,1,taken+1);
            else
            return cache[a][b][prev][taken]=dp(a,b-1,1,taken);
        }
        else
        {
            if(prev==0)
            return cache[a][b][prev][taken]=dp(a-1,b,0,taken);
            else
            return cache[a][b][prev][taken]=dp(a-1,b,0,taken+1);
        }
    }
    public static void path(int a,int b,int prev,int taken)
    {
        if(a==0&&b==0&&taken==x)
        System.exit(0);
        if(a>0&&b>0)
        {
            if(prev==0)
            {
                if(dp(a-1,b,0,taken)>dp(a,b-1,1,taken+1))
                {
                    System.out.print(0);
                    path(a-1,b,0,taken);
                }
                else
                {
                    System.out.print(1);
                    path(a,b-1,1,taken+1);
                }
            }
            else
            {
                if(dp(a-1,b,0,taken+1)>dp(a,b-1,1,taken))
                {
                    System.out.print(0);
                    path(a-1,b,0,taken+1);
                }
                else
                {
                    System.out.print(1);
                    path(a,b-1,1,taken);
                }
            }
        }
        else if(a==0)
        {
            System.out.print(1);
            if(prev==0)
            path(a,b-1,1,taken+1);
            else
            path(a,b-1,1,taken);
        }
        else
        {
            System.out.print(0);
            if(prev==0)
            path(a-1,b,0,taken);
            else
            path(a-1,b,0,taken+1);
        }
    }
    public static void main(String[] args)throws IOException
    {
        PrintWriter out= new PrintWriter(System.out);
        Reader sc=new Reader();
        int a=sc.i();
        int b=sc.i();
        x=sc.i();
        cache=new int[a+2][b+2][2][x+250];
        for(int i=0;i<a+2;i++)for(int j=0;j<b+2;j++)for(int k=0;k<2;k++)
        Arrays.fill(cache[i][j][k],-1);
        int val1=dp(a-1,b,0,0);
        if(val1>0)
        {
            System.out.print(0);
            path(a-1,b,0,0);
            System.exit(0);
        }
        for(int i=0;i<a+2;i++)for(int j=0;j<b+2;j++)for(int k=0;k<2;k++)
        Arrays.fill(cache[i][j][k],-1);
        int val2=dp(a,b-1,1,0);
        if(val2>0)
        {
            System.out.print(1);
            path(a,b-1,1,0);
            System.exit(0);
        }
    }
}