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#JavaScript (ES6), 51

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 l=>l.sort((a,b)=>(a+l).length-(b+l).length||b-a)[0]

**Test**

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<!-- language: lang-js -->

 f=l=>l.sort((a,b)=>(a+l).length-(b+l).length||b-a)[0]

 ;[
 [[1], 1]
 ,[[9], 9]
 ,[[1729], 1729]
 ,[[1, 1], 1]
 ,[[34, 3], 3]
 ,[[38, 39], 39]
 ,[[409, 12, 13], 13]
 ,[[11, 11, 11, 1], 1]
 ,[[11, 11, 11, 11], 11]
 ,[[78, 99, 620, 1], 1]
 ,[[78, 99, 620, 10], 99]
 ,[[78, 99, 620, 100], 99]
 ,[[1, 5, 9, 12, 63, 102], 9]
 ,[[3451, 29820, 2983, 1223, 1337], 3451]
 ,[[738, 2383, 281, 938, 212, 1010], 938]
 ].forEach(([l,x])=>{
 var r=f(l)
 console.log(r==x?'OK':'KO',l+' -> '+r)
 }) 


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