Task

Write a function or program which:

   takes a positive integer representing a duration in seconds as input (e.g., 100), and
   returns a string which shows the same duration decomposed into:
   weeks,
   days, 
   hours, 
   minutes,   and 
   seconds.
This is detailed below (e.g., "2 hr, 59 sec").



Demonstrate that it passes the following three test-cases:

Test Cases


 input number

 output string


 7259

 2 hr, 59 sec


 86400

 1 d


 6000000

 9 wk, 6 d, 10 hr, 40 min

Details
The following five units should be used:



 unit

 suffix used in output

 conversion


 week

 wk

 1 week = 7 days


 day

 d

 1 day = 24 hours


 hour

 hr

 1 hour = 60 minutes


 minute

 min

 1 minute = 60 seconds


 second

 sec



However, only include quantities with non-zero values in the output (e.g., return "1 d" and not "0 wk, 1 d, 0 hr, 0 min, 0 sec").

Give larger units precedence over smaller ones as much as possible (e.g., return 2 min, 10 sec and not 1 min, 70 sec or 130 sec)

Mimic the formatting shown in the test-cases (quantities sorted from largest unit to smallest and separated by comma+space; value and unit of each quantity separated by space).




compoundDuration[x_Integer] := 
 StringJoin @@ (Riffle[
     ToString /@ ((({Floor[x/604800], 
             Mod[x, 604800]} /. {a_, b_} -> {a, Floor[b/86400], 
              Mod[b, 86400]}) /. {a__, b_} -> {a, Floor[b/3600], 
            Mod[b, 3600]}) /. {a__, b_} -> {a, Floor[b/60], 
          Mod[b, 60]}), {" wk, ", " d, ", " hr, ", " min, ", 
      " sec"}] //. {a___, "0", b_, c___} -> {a, c})
 
Grid[Table[{n, "secs =", 
   compoundDuration[n]}, {n, {7259, 86400, 6000000}}], 
 Alignment -> {Left, Baseline}]