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Employee Benefit Plans - Components of Net Periodic Benefit Cost (Details) (USD $)
In Thousands, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Pension benefits      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Service cost $ 850kai_ServiceCostAndOther
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= us-gaap_PensionPlansDefinedBenefitMember
$ 998kai_ServiceCostAndOther
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
$ 991kai_ServiceCostAndOther
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
Interest cost 1,286us-gaap_DefinedBenefitPlanInterestCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
1,167us-gaap_DefinedBenefitPlanInterestCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
1,313us-gaap_DefinedBenefitPlanInterestCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
Expected return on plan assets (1,480)us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
(1,506)us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets
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= us-gaap_PensionPlansDefinedBenefitMember
(1,616)us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
Recognized net actuarial loss 315us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlementsAndCurtailments1
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
533us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlementsAndCurtailments1
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
634us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlementsAndCurtailments1
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
Amortization of prior service cost 55us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
55us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
56us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
Net periodic benefit cost 1,026us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
1,247us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
1,378us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost
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= us-gaap_PensionPlansDefinedBenefitMember
Other Benefits      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Service cost 261kai_ServiceCostAndOther
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
171kai_ServiceCostAndOther
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
143kai_ServiceCostAndOther
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
Interest cost 225us-gaap_DefinedBenefitPlanInterestCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
207us-gaap_DefinedBenefitPlanInterestCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
225us-gaap_DefinedBenefitPlanInterestCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
Expected return on plan assets 0us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
0us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
0us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
Recognized net actuarial loss 34us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlementsAndCurtailments1
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
62us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlementsAndCurtailments1
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
36us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlementsAndCurtailments1
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
Amortization of prior service cost 91us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
85us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
28us-gaap_DefinedBenefitPlanAmortizationOfPriorServiceCostCredit
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
Net periodic benefit cost $ 611us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
$ 525us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember
$ 432us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPensionPlansDefinedBenefitMember