The White House called North Korea the odd man out. President Barack Obama counted it back in.
Billed as a trip about securing dangerous nuclear material, Obama's mission here has morphed into a concentrated and calculated opportunity to warn, cajole and shame North Korea to change course. He has stared down North Korea from an observation post, lectured its leaders, pleaded for them to choose peace and belittled them as living 50 years in the past.
Some of this was bound to happen. By holding a nuclear security summit in South Korea, the world was inviting the shadow of the uninvited neighbor to the north, whose nuclear weapons program, missile testing and murky intentions tend to seize attention. Then the North's plan for a long-range rocket launch unnerved the leaders gathered here.
Obama took it deeper, inviting a showdown rather than dismissing North Korea as distraction. In an imagery-filled visit to the demilitarized no-man's land between North and South, in his comments with the South Korean president, in his appearance before reporters and in his lobbying with China, Obama pounded on North Korea's behavior.
Politically, Obama had little to lose by getting tough on North Korea, but plenty if he didn't. Up for election at home, and promising friends in Asia they are a new focal point of America's strategic interest, Obama's leadership surely would have been scrutinized had he passed up the chance to take a stand while here.
So he exploited the contrast between the surging South and the impoverished North as a symbol of his broader message: a new chance for North Korea to choose hope or oblivion.
Yet this wasn't exactly the story the White House promoted before the president arrived.
The focus had been on the important if uninspiring work of getting more than 50 nations to secure or give up their nuclear material, so that it would not end up with terrorists bent on destroying a city. At the summit, which is the main reason Obama came at all, North Korea is not even directly on the agenda.
"The point here is that president is going to the Nuclear Security Summit. The Nuclear Security Summit is not about North Korea," Daniel Russel, Obama's senior Asia adviser, said in a preview days ago when asked about the North's latest provocations.
"North Korea," he added, "will be the odd man out."
Sidelined, yes, but hardly silenced.
There was an entire parallel agenda across Obama's three days here, both for him and other leaders. Only now, as the summit unfolds in earnest at the end of his stay, will Obama and his peers dive into the nitty gritty of his goal of securing all nuclear material within two more years.
"It's hard enough to keep attention on nuclear security, because there is disagreement on the threat and what to do about it," said Sharon Squassoni, director of the proliferation prevention program at the Center for Strategic and International Studies. And then throw in the distracting effect of North Korea.
"A summit is a completely inappropriate venue for dealing with the North Korean threat," she added. "A summit of 54 leaders is not a negotiating forum."
So instead, North Korea carried its own shadow agenda.
The broad challenge for the United States and its partners has been how to sway North Korea to seek a better version of itself.
The immediate dilemma? What to do about North Korea's planned long-range rocket launch next month. The United States and other nations see it as a cover for testing long-range missiles that could be mounted with nuclear weapons. South Korea underlined the stakes by warning it might shoot down parts of the rocket if it violates its air space.
Obama has been trying to prevent that launch and influence China to show more toughness toward its neighbor, North Korea. Yet he did not want to get drawn into a trap _ one more consuming episode-of-the-moment with a country known for them. So he tried to swing bigger.
"I want to speak directly to the leadership in Pyongyang," Obama declared in a speech. He offered a hand of peace and warned of the consequences of rejection.
"Instead of the dignity you desire, you are more isolated," he said of North Korea's leadership. "Instead of earning the respect of the world, you have been met with strong sanctions. You can continue down the road you are on, but we know where that leads."
Ben Rhodes, a deputy national security adviser to Obama, said it was natural for the president to challenge North Korea's behavior in the context of a broad trip aimed at stopping nuclear proliferation and keeping nuclear material secure.
The White House also came into the trip figuring it was right not to celebrate an apparent breakthrough with North Korea just last month, when North Korea won a U.S. pledge of food aid in return for nuclear and missile test moratoriums. The planned rocket launch scuttled that goodwill.
And Obama has shown little desire to hide his impatience.
He described North Korea's governing leaders this way: They can't feed their people, they don't make anything of use, they have no exports except weapons, and they fail on all indictors of well-being. "You'd think you'd want to try something different," he said.
If they do, and they keep their word, Obama said no one will welcome them more than the United States.
For now, odds are North Korea will remain the odd man out, but never out of the discussion.
White House Correspondent Ben Feller has covered the Obama and Bush presidencies for The Associated Press