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

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- Definition The actuarial present value of benefits attributed by the pension benefit formula to services and other costs rendered by employees during the period. The portion of the expected postretirement benefit obligation attributed to employee service and other during the period. The service and other cost component is a portion of the benefit obligation and is unaffected by the funded status of the plan. + References No definition available. + Details
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- Definition The amount of the prior service cost or credit recognized in net periodic benefit cost relating to benefit changes attributable to plan participants' prior service pursuant to a plan amendment or a plan initiation. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (h)(1) -URI http://asc.fasb.org/extlink&oid=35743120&loc=d3e1928-114920 + Details
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- Definition An amount calculated as a basis for determining the extent of delayed recognition of the effects of changes in the fair value of assets. The expected return on plan assets is determined based on the expected long-term rate of return on plan assets and the market-related value of plan assets. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 30 -Glossary Expected Return on Plan Assets -URI http://asc.fasb.org/extlink&oid=6512136 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 60 -Glossary Expected Return on Plan Assets -URI http://asc.fasb.org/extlink&oid=6512171 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (h)(3) -URI http://asc.fasb.org/extlink&oid=35743120&loc=d3e1928-114920 + Details
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- Definition The increase in a defined benefit pension plan's projected benefit obligation or a defined benefit postretirement plan's accumulated postretirement benefit obligation due to the passage of time. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (h)(2) -URI http://asc.fasb.org/extlink&oid=35743120&loc=d3e1928-114920 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (a)(2) -URI http://asc.fasb.org/extlink&oid=35743120&loc=d3e1928-114920 + Details
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- Definition The total amount of net periodic benefit cost for defined benefit plans for the period. Periodic benefit costs include the following components: service cost, interest cost, expected return on plan assets, gain (loss), prior service cost or credit, transition asset or obligation, and gain (loss) due to settlements or curtailments. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (j) -URI http://asc.fasb.org/extlink&oid=35743120&loc=d3e1928-114920 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (h) -URI http://asc.fasb.org/extlink&oid=35743120&loc=d3e1928-114920 + Details
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- Definition Amount of net gain (loss) recognized in net periodic benefit cost due to settlements and curtailments. Curtailments result from an event that significantly reduces the expected years of future service of present employees or eliminates for a significant number of employees the accrual of defined benefits for some or all of their future services. Settlements result from an irrevocable action that relieves the employer (or the plan) of primary responsibility for a benefit obligation and eliminates significant risks related to the obligation and the assets used to effect the settlement. Examples of transactions that constitute a settlement include, but are not limited to, lump-sum cash payments to plan participants in exchange for their rights to receive specified benefits and purchasing nonparticipating annuity contracts to cover vested benefits. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (h)(7) -URI http://asc.fasb.org/extlink&oid=35743120&loc=d3e1928-114920 + Details
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