SEOUL—As North and South Korea prepare to hold their first official, face-to-face talks in two years, the stakes have rarely been higher.

The North, now under the tightest sanctions yet, has rapidly advanced its weapons program in the past year and claims to be able to hit the U.S. with nuclear-armed ballistic missiles. Leaders in Pyongyang and Washington have openly threatened nuclear war. Against this backdrop, the South is five weeks away from hosting the Olympic Games.

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