I am not able to understand dp state in MERGEBS

Que Link: Merging Binary Strings | CodeChef

My 1st solution: Solution: 56711236 | CodeChef

My approach:
traversing both string from right to left
if in any string I find ‘1’ than I will consider that 1 other wise I will minimize my ans.
result: WA in all test case

My 2nd solution (just trial and error): Solution: 56734235 | CodeChef
Every time minimize ans.
result: Worked in smaller test case. (TLE for rest)

Even if I don’t consider larger test case why my 1st solution isn’t working?