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. 
from itertools import accumulate
import os
import sys
from io import BytesIO, IOBase
import math

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)


def input(): return sys.stdin.readline().rstrip("\r\n")


# ------------------- fast io --------------------
a,b,x=map(int,input().split())
if x==1:
    ans=""
    for i in range(a):
        ans+="0"
    for i in range(b):
        ans+="1"
    print(ans)
else:
    ans=""
    x=x-1
    if a>=b:
        ans="0"
        count=x
        a-=1
        c=0
        while(count>0):
            if c%2==0:
                ans+="1"
                b-=1
                count-=1
                c=1
            else:
                ans+="0"
                count-=1
                a-=1
                c=0
        if ans[-1]=="0":
            for i in range(a):
                ans+="0"
            for i in range(b):
                ans+="1"
        else:
            for i in range(b):
                ans+="1"
            for i in range(a):
                ans+="0"
        print(ans)
    else:
        ans = "1"
        count = x
        b -= 1
        c = 0
        while(count > 0):
            if c % 2 == 0:
                ans += "0"
                a -= 1
                count -= 1
                c = 1
            else:
                ans += "1"
                count -= 1
                b -= 1
                c = 0
        if ans[-1] == "0":
            for i in range(a):
                ans += "0"
            for i in range(b):
                ans += "1"
        else:
            for i in range(b):
                ans += "1"
            for i in range(a):
                ans += "0"
        print(ans)
            
            
        
