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There is no cause to pass the TLE. Because the complexity of your algorithm is O(n). Just look at the line of the problem statement. Each line contains a single 64-nit signed integer which denotes the value of n. Your can't pass TLE with complexity of O(sqrt(n)) or O(lg n). You must find result in e...

Can anyone tell me how can i solve it without passing the TLE (Within 5 seconds during the onsite contest).
I cannot figure out DP or direct formula for this problem.
Thnx in advance.

You needn't use string to find only the result. There is great symmetry. Just gets your hands dirty by some input and output. This is easy to find the symmetry (you will find same result after specific range that is very small). So, you needn't trace the number just look at the last two digits.

I haven't tried it yet & have no time to have a try. But, have you tried Code:
1 0 1 0 1 0


for Code:
0


?

Don't ask me "WHY ?"......

Yes. i tried all possible output for input 0. But always got wa.

Ya, you can use combinatorics. But for the length(s) = 7, it is bit harder.
I also use combinatorics, but get wrong answer several time but didn't know why. At last, I get accepted using backtracking (Complete brutforce).

Try with the input:
1
12

Output will be:
26

I can't understand what you want to do. Please, explain more, because i am trying to solve this problem but still failure. (LAST POST)
Edited:
Because I could not the manage the sign of the triangle so the output will different than expected. Finally I success.

Thnx everybody who posted.

I found my mistake and got accepted. Thnx to all viewers. So i post the correct output for some input and output: INPUT: 0 4 99 100 OUTPUT: 0 0 0 0 0 0 30 70 100 900 354 9646 328350 24174150 24502500 121262872500 1950333330 600370555916670 338350 25164150 25502500 128762122500 2050333330 65037545591...