Genius's Gambit

Description:

Input:

The only line contains three integers $$$a$$$, $$$b$$$, and $$$k$$$ ($$$0 \leq a$$$; $$$1 \leq b$$$; $$$0 \leq k \leq a + b \leq 2 \cdot 10^5$$$) — the number of zeroes, ones, and the number of ones in the result.

Output:

If it's possible to find two suitable integers, print "Yes" followed by $$$x$$$ and $$$y$$$ in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Sample Input:

4 2 3

Sample Output:

Yes
101000
100001

Sample Input:

3 2 1

Sample Output:

Yes
10100
10010

Sample Input:

3 2 5

Sample Output:

No

Note:

In the first example, $$$x = 101000_2 = 2^5 + 2^3 = 40_{10}$$$, $$$y = 100001_2 = 2^5 + 2^0 = 33_{10}$$$, $$$40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}$$$. Hence $$$x-y$$$ has $$$3$$$ ones in base-2.

In the second example, $$$x = 10100_2 = 2^4 + 2^2 = 20_{10}$$$, $$$y = 10010_2 = 2^4 + 2^1 = 18$$$, $$$x - y = 20 - 18 = 2_{10} = 10_{2}$$$. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.