Greedy
Discard what can never help, then combine
A one-line filter that makes the rest of the problem trivial, and the argument for why it is safe.
Key idea
Combining takes the larger of each component
You have several tuples, and combining two produces the componentwise maximum. Starting from any of them and combining freely, can you reach a given target?
Searching over which to combine is exponential. There is a one-pass answer, and the whole difficulty is the filter.
Why it works
A tuple exceeding the target anywhere is poison
Because combining only ever raises components and never lowers them, any tuple with a component larger than the target's can never be part of a solution. Including it makes that component permanently too large.
So discard those first. What remains cannot overshoot in any component, which means combining all of them is safe and gives the largest reachable value in every component simultaneously.
That is the argument: filtering is safe because the operation is monotone, and after filtering there is no reason to be selective, so take everything.
The filter is the whole difficulty, so here it is on its own, with each tuple judged against the target.
Tip
After filtering, there is nothing to decide
It is tempting to look for the right subset to combine. There is none to find: every surviving tuple can only help, since it cannot overshoot and might raise a component that is still short.
Recognizing that a decision has disappeared is worth as much as making it well. When an operation is monotone and the invalid options have been removed, take everything that is left.
Gotcha
Every component must be reached exactly
The final check compares the whole combined tuple against the target. Checking only that no component is short would accept an overshoot, and checking only one component would accept a partial match.
Because the filter already prevents overshooting, equality and not-short are the same condition here, and writing the equality makes the intent obvious and survives changes to the filter.
Edge cases
Starting from nothing
The accumulator starts at zeros, which represents having combined nothing yet. If the target contains a zero component, that is reachable only if no surviving tuple raises it, which the maximum handles naturally.
If every tuple is filtered out, the accumulator stays at zeros and the comparison correctly reports failure unless the target is itself all zeros. Worth checking rather than assuming.
Predict the output: why one bad component is fatal
Combining two tuples takes the larger value in each position. A tuple that already exceeds the target somewhere is combined anyway, to see what happens. Type the three lines it prints.
Merge Triplets To Form Target Triplet
Read the constraints first and let them tell you what complexity is expected. Derive the approach, implement it, run the tests, and submit when it passes.