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sub solution_1 {
    # queue solution
    # O(2*N+M) memory, O(N^2*M) time
...
    pop @queue;
    print OUT "$_\n" for @queue;
}

Benchmark: timing 100 iterations of Baseline, LR_1, LR_2, Queue...
  Baseline: 0.555567 wallclock secs ( 0.55 usr +  0.00 sys =  0.55 CPU
+) @ 181.82/s (n=100)
            (warning: too few iterations for a reliable count)
...
LR_1     13889/s      13%       --     -41%     -78%
Queue    23474/s      91%      69%       --     -62%
Baseline 62112/s     404%     347%     165%       --