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 collections
from statistics import mean
max=0

def calc(s):
    c=0
    for i in range(len(s)-1):
        if s[i]!=s[i+1]:
            c+=1
    return c


s=input().split()
a,b,x=int(s[0]),int(s[1]),int(s[2])
#print((x//2))

def makeString(s,x):
    i=1
    if(s=="0"):
        one,zero=0,1
    else:
        one,zero=1,0
    while(i<x):
        if s[i-1]=="0":
            s=s+"1"
            one+=1
        else:
            s=s+"0"
            zero+=1
        i+=1
    #print(s)
    if s[len(s)-1]=="0":
        s+=((a-zero)*"0")+((b-one)*"1")
    else:
        s+=((b-one)*"1")+((a-zero)*"0")
    return s

s1=makeString("0",x)
s2=makeString("1",x)

if calc(s1)==x:
    print(s1)
else:
    print(s2)