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r - Replace value with the name of its respective column

I have a data frame:

Code    401k    CVS
101A            true
231N    true
FD54    true
99JB    
85F4    true

I'm trying to replace the "true" character values with the respective column name (e.g. "401k"). This is my desired output:

Code    401k    CVS
101A            CVS
231N    401k
FD54    401k
99JB    
85F4    401k
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The coding below enabled me to replace every "true" value (character) into its respective column name.

##Replace every "true" value with its respective column name
w <- which(df=="true",arr.ind=TRUE)
df[w] <- names(df)[w[,"col"]]

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