In this Aug. 25, 2016, file photo, a South Korean army soldier watches a TV news program, which shows images published in North Korea's Rodong Sinmun newspaper of North Korea's ballistic missile and North Korean leader Kim Jong Un, in Seoul. (Ahn Young-Joon/Associated Press)

When South Korean officials talk about the growing nuclear challenge from North Korea, they use red-alert phrases such as “existential threat,” “imminent danger” and “dagger at the throat.” They want Americans to understand that this long-running story of brinkmanship has entered a new phase.

One senior South Korean official told me starkly: “A nuclear missile from the North can land on this office in four to five minutes. We don’t have the luxury of thinking twice. . . . This is no longer a dark cloud on the horizon. It’s a threat at our doorstep.”

A few miles away at U.S. Army Garrison Yongsan , where U.S. troops are headquartered, a senior U.S. military officer offered a similar warning. He noted that the base, like most of Seoul, has lived for decades under threat from North Korean artillery across the demilitarized zone, but he said the nuclear menace is different: “This is not just a throwback to the Korean War. It’s an evolving threat that is becoming dangerous outside the Korean Peninsula.”

These conversations illustrate why the North Korean nuclear issue may top the security worries of the next U.S. president. There’s a sense here, among South Korean and American officials alike, that Kim Jong Un, the mercurial leader in Pyongyang, is racing through the warning lights to gain nuclear weapons and missile capabilities to attack his neighbors, and also the United States. The next U.S. president will have to decide what to do about it.

“What North Korea wants is what it can’t get, which is acceptance as a nuclear weapons state,” argued Christopher Hill, a former U.S. ambassador who headed the unsuccessful six-party talks with North Korea in 2005-2007. He was speaking at the World Knowledge Forum conference here.

The frustration voiced by U.S. and South Korean officials is that nothing has succeeded in checking North Korea’s relentless advance toward nuclear weapons. Diplomatic talks, U.N. economic sanctions and threats of military force have all failed. North Korea is a pitifully backward country, except in its nuclear and missile programs.

Even China seems to have limited leverage. Many analysts think Beijing could successfully pressure North Korea. But although the Chinese sent a special emissary last year to warn against a fourth nuclear test, the regime went ahead with a test in January. Beijing then supported a U.N. Security Council resolution in March condemning North Korea and imposing sanctions, and Kim responded with a fifth nuclear test last month.

How should the United States work with Seoul to combat this intractable problem? Some leading South Korean officials offered useful suggestions.

Tightening sanctions is a first step. U.S. Ambassador to the United Nations Samantha Power was just here discussing a new resolution to do that. South Korea hopes the United Nations will close the “livelihood” exemption that allows North Korea to export coal to China. Coal exports totaled about $1 billion last year and are a major source of foreign exchange to finance the nuclear program. The Chinese have so far balked at squeezing their neighbor harder.

Driving a wedge between Kim and members of his government elite is another South Korean proposal. President Park Geun-hye told her cabinet this week that a recent increase in high-level defections shows the fragility of Kim’s regime — and that South Korea should encourage even more defectors. Seoul’s message is that if Kim keeps subordinating all other concerns to his nuclear ambition, the regime will eventually implode.

Deterring North Korea militarily is what South Korea wants most from the United States. Park has agreed to installation of the U.S. THAAD missile-defense system , but that won’t be ready until December 2017. South Korean officials hope the United States can reassure a jittery public about the reliability of its nuclear umbrella — politely termed “extended deterrence.” That could mean more overflights by B-52 and B-1 bombers, more visits by top U.S. officials and more joint defense talks like those scheduled in Washington next week.

Restarting diplomacy with Pyongyang gets little public support here, but South Korea and the United States have left the door open. One face-saving approach would be secret, preliminary U.S. talks with North Korea that would lead later, in concert with China, to public talks about denuclearization. But there’s no sign North Korea wants such a dialogue.

What happens if all these efforts fail, and Kim deploys nuclear-tipped missiles that could hit U.S. territory? “We should have a euphemism for ‘preemption,’ ” commented one former senior U.S. official at the conference here.

But whatever word is used, an unpalatable military choice may confront the next president — for the simple reason that nothing else seems to have worked.

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