Last Updated Mar 5, 2016 5:42 PM EST

5:40 p.m. ET Fifty-three percent of Kansas caucus results are in and CBS News is projecting a winner: Texas Sen. Ted Cruz.

At a rally in Idaho, Cruz addressed the results, saying “God bless Kansas. And God bless Maine.”

5:25 p.m. With 42 percent of Kansas caucus results in, Texas Sen. Ted Cruz maintains his lead.

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5:20 p.m.With 31 percent of the vote in, Ted Cruz is leading Donald Trump in Kansas by double digits.

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5 p.m. On Saturday, Kansas Republicans met at more than 100 caucus locations to cast secret ballots for the party’s presidential nomination.

The state GOP party reported lines out the door in some caucus locations, even calling the turnout on Saturday “incredible” in one tweet.

At one caucus site in Shawnee Mission South, GOP officials reportedly ran out of printed ballots and resorted to casting votes on notecards, according to a Kansas City Star report.

Donald Trump made a last-minute push for Kansas supporters on Saturday, cramming in an extra campaign rally before the caucus and skipping the Conservative Political Action Conference in Maryland to do so. Trump was scheduled to speak at CPAC early Saturday but announced the day before that he would hold a rally in Wichita, Kansas, instead.

Though polling was scarce for Kansas, the state’s closed contest — which prevents Democrats from switching parties to vote in the Republican caucus — meant lowered predictions for Trump support. Of the last four closed primary states (the Iowa caucus, the Nevada caucus and Super Tuesday’s Oklahoma primary and Alaska caucus) Ted Cruz won three of those contests. Trump, meanwhile, has fared better in open primaries.

Three other states vote Saturday in the Republican primary race: Kentucky, Louisiana, and Maine. Saturday’s states have a total of 155 delegates up for grabs.