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. 
#    !/usr/bin/env python3
#    encoding: UTF-8
#    Modified: <16/Oct/2019 11:35:36 AM>


#    ✪ H4WK3yE乡
#    Mohd. Farhan Tahir
#    Indian Institute Of Information Technology (IIIT), Gwalior


import sys
import os
from io import IOBase, BytesIO


def main():
    a, b, x = get_ints()
    f = 1
    if x & 1:
        f = 0
    if f == 0:
        s = "0"
        a -= 1
        while x > 0:
            if b == 0:
                break
            s += "1"
            b -= 1
            x -= 1
            if x > 0:
                if a == 0:
                    break
                s += "0"
                a -= 1
                x -= 1
        zero = "0" * a
        one = "1" * b
        print(zero + s + one)
    else:
        if a >= b:
            s = "0"
            a -= 1
            while x > 0:
                if b == 0:
                    break
                s += "1"
                b -= 1
                x -= 1
                if x > 0:
                    if a == 0:
                        break
                    s += "0"
                    a -= 1
                    x -= 1
            l = list(s)
            l.pop()
            zero = "0" * a
            one = "1" * b
            tmp = ""
            for i in l:
                tmp += i
            print(zero + tmp + one + "0")

        else:
            s = "1"
            b -= 1
            while x > 0:
                if a == 0:
                    break
                s += "0"
                a -= 1
                x -= 1
                if x > 0:
                    if b == 0:
                        break
                    s += "1"
                    b -= 1
                    x -= 1
            l = list(s)
            l.pop()
            zero = "0" * a
            one = "1" * b
            tmp = ""
            for i in l:
                tmp += i
            print(one + tmp + zero + "1")


BUFSIZE = 8192


class FastIO(BytesIO):
    newlines = 0

    def __init__(self, file):
        self._file = file
        self._fd = file.fileno()
        self.writable = "x" in file.mode or "w" in file.mode
        self.write = super(FastIO, self).write if self.writable else None

    def _fill(self):
        s = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
        self.seek((self.tell(), self.seek(0, 2), super(FastIO, self).write(s))[0])
        return s

    def read(self):
        while self._fill():
            pass
        return super(FastIO, self).read()

    def readline(self):
        while self.newlines == 0:
            s = self._fill()
            self.newlines = s.count(b"\n") + (not s)
        self.newlines -= 1
        return super(FastIO, self).readline()

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


class IOWrapper(IOBase):
    def __init__(self, file):
        py2 = round(0.5)
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        if py2 == 1:
            self.write = self.buffer.write
            self.read = self.buffer.read
            self.readline = self.buffer.readline
        else:
            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 get_array():
    return list(map(int, sys.stdin.readline().split()))


def get_ints():
    return map(int, sys.stdin.readline().split())


def input():
    return sys.stdin.readline().strip()


if __name__ == "__main__":
    main()
