There are a multitude of ways North Korea could deliver a nuclear bomb to South Korea. It does not have to be by missile. Tunnel, suicide airplane, boat, truck.
Nor does it have to be by ICBM to nuke the US. A small boat sailed into any harbor could do the trick. We have over 80,000 miles of unprotected coastline.
Where there's a will, there's a way.
So how should we respond?
Russia threatened us with nukes for over 40 years. I grew up under that threat, and I served in the military under that threat, so Korea's saber rattling is not that intimidating to me.
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I also served during that period but I do not ever recall Russia verbally threatening us with a preemptive strike. We both realized that if one struck the other would return the same.