Why is the Mantel-Haenszel test returning a confidence interval of infinity?

Question

When I set alternative = "greater" when using a mantelhaen.test, the upper confidence interval returned is Inf. Why does this happen, and can I fix it? I'm not sure if this issue is rooted in the programming (maybe the format of my data?) or if it's more of a statistics question.

Here's my output:

       Mantel-Haenszel chi-squared test with continuity correction

    Mantel-Haenszel X-squared = 3.7413, df = 1, p-value = 0.02654
    alternative hypothesis: true common odds ratio is greater than 1
    95 percent confidence interval:
     1.192457      Inf
    sample estimates:
    common odds ratio 
      2.59944 

Here's some example code to demonstrate:

    library(vcd)
    library(DescTools)

    example =("
                      Year Treatment Dead      Count
                      2015  Control   no          50
                      2015  Treat     no          60
                      2015  Control   yes          1
                      2015  Treat     yes          4
                      2016  Control   no          40                                  
                      2016  Treat     no         115                
                      2016  Control   yes          2                  
                      2016  Treat     yes          9 
                      2017  Control   no         142                 
                      2017  Treat     no          33      
                      2017  Control   yes          6                 
                      2017  Treat     yes          5                 
                      ")

    example = read.table(textConnection(example),header=TRUE)

    example =
      mutate(example,
             Year = factor(Year, levels=unique(Year)),
             Treatment = factor(Treatment, levels=unique(Treatment)),
             Dead = factor(Dead, levels=unique( Dead))
      )

    example.xtabs = xtabs(Count ~ Dead + Treatment + Year, 
                                  data=example)   


    ftable(example.xtabs)                      


    mantelhaen.test(example.xtabs) 
    mantelhaen.test(example.xtabs, alternative = "greater") #one sided - why 
                                                             #does CI = Inf