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. 
# PREFUNCS
def inline():
    return [ int(e) for e in input().split() ]

def outline(l):
    for e in l: print(e, end=" ")
    print()

def outlist(l):
    for e in l: print(e)



# FUNCTIONS
def insert(s, p, i):
    return s[:p] + i + s[p:]

def zig(a, b, x):
    z = str()
    turn = False
    if a > b:
        z += '0'
        a -= 1
        turn = True
    else: 
        z += '1'
        b -= 1
    while x > 0:
        if turn:
            z += '1'
            b -= 1
            x -= 1
            turn = not turn
        else:
            z += '0'
            a -= 1
            x -= 1
            turn = not turn
    return [a, b, z]
        


# INPUT
inp = inline()
a = inp[0]
b = inp[1]
x = inp[2]



# PROCESS
z = zig(a, b, x)
s = z[-1]

a = z[0]
b = z[1]
if a > 0:
    for i in range( len(s) ):
        if s[i] == '0':
            s = insert(s, i, '0' * a)
            break
if b > 0:
    for i in range( len(s) ):
        if s[i] == '1':
            s = insert(s, i, '1' * b)
            break    



# OUTPUT
print(s)