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 $1 \le i < n$) such that $s_i \ne s_{i + 1}$. It is guaranteed that the answer always exists.

For example, for the string "01010" there are four indices $i$ such that $1 \le i < n$ and $s_i \ne s_{i + 1}$ ($i = 1, 2, 3, 4$). 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 $x$ ($1 \le a, b \le 100, 1 \le x < a + b)$.


-----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.

Difficulty: introductory

Starter code:

Solutions:

a,b,x=list(map(int,input().split()))
if(a>b):
    s='0'
    a-=1
else:
    s='1'
    b-=1
for i in range(x-1):
    if(s[-1]=='1'):
        s+='0'
        a-=1
    else:
        s+='1'
        b-=1
if(s[-1]=='1'):
    s+='1'*(b)
    s+='0'*a
else:
    s+='0'*a
    s+='1'*b
print(s)



(a, b, x) = list(map(int, input().split()))
n = a + b

if a > b:
    s = '0'
    a -= 1
else:
    s = '1'
    b -= 1

for i in range(1, n):
    if x > 1:
        if s[i - 1] == '0':
            s = s + '1'
            b -= 1
        else:
            s = s + '0'
            a -= 1
        x -= 1
    elif s[i - 1] == '0':
        if a > 0:
            s = s + '0'
            a -= 1
        else:
            s = s + '1'
            b -= 1
    else:
        if b > 0:
            s = s + '1'
            b -= 1
        else:
            s = s + '0'
            a -= 1

print(s)


a, b, x = list(map(int, input().split()))
if a > b:
    c = 0
else:
    c = 1
for i in range(x):
    print(c, end='')
    if i == x-1:
        if c == 0:
            print("0"*(a-1), end='')
            a = 0
        else:
            print("1"*(b-1), end='')
            b = 0
    if c == 0:
        a -= 1
    else:
        b -= 1
    c ^= 1
print("1"*b, end='')
print("0"*a, end='')


a, b, x = map(int, input().split())

if a > b:
    print(0, end='')
    prev = 0
    a -= 1
else:
    print(1, end='')
    prev = 1
    b -= 1

for i in range(x - 1):
    if prev == 0:
        print(1, end='')
        prev = 1
        b -= 1
    else:
        print(0, end='')
        prev = 0
        a -= 1

if prev == 0:
    for i in range(a):
        print(0, end='')
    
    for i in range(b):
        print(1, end='')

else:
    for i in range(b):
        print(1, end='')
        
    for i in range(a):
        print(0, end='')

a,b,x=list(map(int,input().split(' ')))
ans=""
if a>b:
    s="01"
    ans+=s*(x//2)
    if x%2==0: 
        ans+="1"*(b-x//2)
        ans+="0"*(a-x//2)
    else:
        ans+="0"*(a-x//2)
        ans+="1"*(b-x//2)    
else:
    s="10"
    ans+=s*(x//2)
    if x%2==0: 
        ans+="0"*(a-x//2)
        ans+="1"*(b-x//2)
    else:
        ans+="1"*(b-x//2)
        ans+="0"*(a-x//2)
print(ans)


a, b, x = list(map(int, input().split()))
mn = "0"
mncnt = a
mx = "1"
mxcnt = b
res = ""
if a > b:
    mn, mx = mx, mn
    mncnt = b
    mxcnt = a
if x % 2 == 0:
    res += (mx+mn)*(x//2)
    res += mn*(mncnt-x//2)
    res += mx*(mxcnt-x//2)
else:
    res += (mx+mn)*(x//2)
    res += mx * (mxcnt - (x//2))
    res += mn * (mncnt - (x//2))
print(res)