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Employee Benefit Plans - Additional Information (Details) (USD $)
12 Months Ended 0 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Sep. 15, 2014
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Number of shares available for grant 689,401us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant      
Share price $ 42.38us-gaap_SharePrice      
Cost recognized, defined contribution plan $ 2,655,000us-gaap_DefinedContributionPlanCostRecognized $ 2,607,000us-gaap_DefinedContributionPlanCostRecognized $ 2,466,000us-gaap_DefinedContributionPlanCostRecognized  
Tax benefits related to employees' and directors' stock plans 771,000us-gaap_AdjustmentsToAdditionalPaidInCapitalTaxEffectFromShareBasedCompensation 351,000us-gaap_AdjustmentsToAdditionalPaidInCapitalTaxEffectFromShareBasedCompensation 132,000us-gaap_AdjustmentsToAdditionalPaidInCapitalTaxEffectFromShareBasedCompensation  
Chief financial officer        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Compensation expense for arrangement with CFO       360,000us-gaap_DeferredCompensationArrangementWithIndividualCompensationExpense
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ChiefFinancialOfficerMember
Pension benefits        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Future amortization of gain (loss) (527,000)us-gaap_DefinedBenefitPlanFutureAmortizationOfGainLoss
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
     
Future amortization of prior service cost (credit) 147,000us-gaap_DefinedBenefitPlanFutureAmortizationOfPriorServiceCostCredit
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
     
Estimated future employer contribution, next year 1,080,000us-gaap_DefinedBenefitPlansEstimatedFutureEmployerContributionsInNextFiscalYear
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
     
Debt securities | Pension benefits        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Maximum weighted-average maturity, debt securities 10 years      
Average benchmark duration for debt securities 5 years      
Restricted stock units for non employee directors (RSUs)        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Grants in period 5,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember
     
Restricted stock units for non employee directors change of control        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Grants in period 10,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= kai_RestrictedStockUnitsForNonEmployeeDirectorsChangeOfControlMember
     
Number of unvested awards 50,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= kai_RestrictedStockUnitsForNonEmployeeDirectorsChangeOfControlMember
     
Fair value of RSU's outstanding 1,009,000kai_AggregateFairValueOfRsuSOutstanding
/ us-gaap_AwardTypeAxis
= kai_RestrictedStockUnitsForNonEmployeeDirectorsChangeOfControlMember
     
Performance shares        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Number of installment vesting periods 3kai_SharebasedCompensationArrangementbySharebasedPaymentAwardNumberofInstallmentVestingPeriods
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
     
Compensation cost not yet recognized 1,413,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
     
Compensation cost not yet recognized, recognition period 1 year 2 months 12 days      
Time-based restricted stock units        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Compensation cost not yet recognized 2,265,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= kai_TimeBasedRestrictedStockUnitsMember
     
Compensation cost not yet recognized, recognition period 1 year 9 months 18 days      
Restricted stock united and stock option awards | Chief financial officer        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Compensation and options expense for arrangement with CFO       428,000kai_DeferredCompensationArrangementwithIndividualCompensationandOptionsExpense
/ us-gaap_AwardTypeAxis
= kai_RestrictedStockUnitsandStockOptionsAwardsMember
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ChiefFinancialOfficerMember
Restricted stock unit awards        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Weighted average grant date fair value, granted (in dollars per share) $ 38.52us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
$ 25.53us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
$ 21.95us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
 
Grants in period 155,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
     
Number of unvested awards 310,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
343,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
   
Fair value of awards vested in period 6,895,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
4,997,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
3,321,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
 
Weighted-average grant date fair value $ 28.06us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
$ 22.50us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
   
Restricted stock unit awards | Chief financial officer        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Grants in period       12,313us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ChiefFinancialOfficerMember
Weighted-average grant date fair value       $ 39.94us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ChiefFinancialOfficerMember
Stock option awards        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Number of installment vesting periods 3kai_SharebasedCompensationArrangementbySharebasedPaymentAwardNumberofInstallmentVestingPeriods
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
     
Compensation cost not yet recognized 589,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
     
Compensation cost not yet recognized, recognition period 1 year      
Award vesting period 3 years      
Weighted-average grant date fair value of options, granted in period   $ 11.33us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 11.69us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
 
Stock option awards | Chief financial officer        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Grants in period       5,201us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ChiefFinancialOfficerMember
Weighted-average grant date fair value of options, granted in period       $ 17.96us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ChiefFinancialOfficerMember
Employee Stock Purchase Plan Awards        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Discount to market under the ESOP 15.00%kai_EmployeeStockOwnershipPlanEsopDiscountToMarket
/ us-gaap_AwardTypeAxis
= kai_EmployeeStockPurchasePlanAwardsMember
     
Maximum period of restriction on resale under ESOP 1 year      
Maximum participation based on compensation percentage under ESOP 10.00%kai_EmployeeStockPurchasePlanEsppMaximumParticipationBasedOnCompensationPercentage
/ us-gaap_AwardTypeAxis
= kai_EmployeeStockPurchasePlanAwardsMember
     
Stock issued during period under ESOP 12,017us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans
/ us-gaap_AwardTypeAxis
= kai_EmployeeStockPurchasePlanAwardsMember
16,325us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans
/ us-gaap_AwardTypeAxis
= kai_EmployeeStockPurchasePlanAwardsMember
17,490us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans
/ us-gaap_AwardTypeAxis
= kai_EmployeeStockPurchasePlanAwardsMember
 
Selling, general and administrative expenses        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Stock-based compensation expense 5,813,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
5,216,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
4,766,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
 
Selling, general and administrative expenses | Restricted stock unit awards        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Stock-based compensation expense 4,904,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
4,102,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
3,731,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
 
Selling, general and administrative expenses | Stock option awards        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Stock-based compensation expense 782,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
1,015,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
954,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
 
Selling, general and administrative expenses | Employee Stock Purchase Plan Awards        
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]        
Stock-based compensation expense $ 127,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= kai_EmployeeStockPurchasePlanAwardsMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
$ 99,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= kai_EmployeeStockPurchasePlanAwardsMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember
$ 81,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= kai_EmployeeStockPurchasePlanAwardsMember
/ us-gaap_IncomeStatementLocationAxis
= us-gaap_SellingGeneralAndAdministrativeExpensesMember