| Pay vs Performance Disclosure | 12 Months Ended |
| Dec. 30, 2023 | Dec. 31, 2022 USD ($) $ / shares | Jan. 01, 2022 USD ($) $ / shares | Jan. 02, 2021 USD ($) $ / shares |
| Pay vs Performance Disclosure | | | | |
| Pay vs Performance Disclosure, Table | Value of Initial Fixed $100 Investment Based On: Year (1) (a) Summary Compensation Table Total for PEO (2) (b) Compensation Average Summary CompensationTable Total for Non-PEO NEOs (2) (d) Average CompensationActually Paid KTB Total S&P 1500 KTB GAAP Net Income ($mm) KTB Adjusted EPS Measure (3) (i) 2023 $[ ] $[ ] $[ ] $[ ] $[ ] $[ ] $[ ] $[ ] 2022 $11,412,428 $10,260,831 $3,175,275 $3,052,820 $104.55 $125.35 $245,493,000 $4.49 2021 $9,979,870 $14,670,445 $2,375,813 $2,881,053 $127.77 $129.18 $195,423,000 $4.28 2020 $6,222,014 $5,305,530 $1,742,947 $1,485,725 $98.08 $111.33 $67,923,000 $2.61 | | | |
| Company Selected Measure Name | Adjusted EPS | | | |
| Named Executive Officers, Footnote | Our Chief Executive Officer, Scott H. Baxter, served as our Principal Executive Officer (“PEO”) in 2023, 2022, 2021 and 2020. Our other NEOs (“Non-PEO NEOs”) included: a. For 2023, Joseph A. Alkire (who served for four months in 2023), Thomas L. Doerr, Jr, Thomas E. Waldron, Christopher M. Waldeck, and Rustin E. Welton. b. For 2022, Thomas L. Doerr, Jr. (who served for seven months in 2022), Thomas E. Waldron, Christopher M. Waldeck, and Rustin E. Welton. c. For 2021, Laurel Krueger (who served for eight months in 2021), Thomas E. Waldron, Christopher M. Waldeck, and Rustin E. Welton. d. For 2020, Laurel Krueger, Thomas E. Waldron, Christopher M. Waldeck, and Rustin E. Welton. | | | |
| PEO Total Compensation Amount | | $ 11,412,428 | $ 9,979,870 | $ 6,222,014 |
| PEO Actually Paid Compensation Amount | | 10,260,831 | 14,670,445 | 5,305,530 |
| Adjustment To PEO Compensation, Footnote | The Company has identified Adjusted EPS as the company-selected measure for the pay versus performance disclosure, representing the most important financial performance measure used to link compensation actually paid to the PEO and the other NEOs in 2023 to the Company's performance. See “Appendix B-Reconciliation of Adjusted Financial Measures” at the end of this document for a reconciliation to the most directly comparable GAAP measure. 2023 2022 2021 2020 Reconciliation of Summary Compensation Totals and Compensation Actual Paid PEO Average Non-PEO NEOs PEO Average PEO Average PEO Average Summary Compensation Table Total for PEO (column (b)) $[ ] $[ ] $11,412,428 $3,175,275 $9,979,870 $2,375,813 $6,222,014 $1,742,947 +/- Net Change in Pension $0 $0 $0 $0 $0 $0 $0 $0 +/- Net Change in Stock Awards $[ ] $[ ] $(1,151,597) $(122,455) $4,630,601 $505,862 $(772,162) $(235,664) +/- Net Change in Option Award $0 $0 $0 $0 $59,974 $(622) $(144,322) $(21,558) Compensation Actually Paid $[ ] $[ ] $10,260,831 $3,052,820 $14,670,445 $2,881,053 $5,305,530 $1,485,725 | | | |
| Non-PEO NEO Average Total Compensation Amount | | 3,175,275 | 2,375,813 | 1,742,947 |
| Non-PEO NEO Average Compensation Actually Paid Amount | | 3,052,820 | 2,881,053 | 1,485,725 |
| Adjustment to Non-PEO NEO Compensation Footnote | The Company has identified Adjusted EPS as the company-selected measure for the pay versus performance disclosure, representing the most important financial performance measure used to link compensation actually paid to the PEO and the other NEOs in 2023 to the Company's performance. See “Appendix B-Reconciliation of Adjusted Financial Measures” at the end of this document for a reconciliation to the most directly comparable GAAP measure. 2023 2022 2021 2020 Reconciliation of Summary Compensation Totals and Compensation Actual Paid PEO Average Non-PEO NEOs PEO Average PEO Average PEO Average Summary Compensation Table Total for PEO (column (b)) $[ ] $[ ] $11,412,428 $3,175,275 $9,979,870 $2,375,813 $6,222,014 $1,742,947 +/- Net Change in Pension $0 $0 $0 $0 $0 $0 $0 $0 +/- Net Change in Stock Awards $[ ] $[ ] $(1,151,597) $(122,455) $4,630,601 $505,862 $(772,162) $(235,664) +/- Net Change in Option Award $0 $0 $0 $0 $59,974 $(622) $(144,322) $(21,558) Compensation Actually Paid $[ ] $[ ] $10,260,831 $3,052,820 $14,670,445 $2,881,053 $5,305,530 $1,485,725 | | | |
| Compensation Actually Paid vs. Company Selected Measure | Relationship Between Compensation Actually Paid and Performance Measures Period Compensation Actually Average compensation KTB TSR Peer Group TSR GAAP Net Adjusted EPS 2020 to 2023 [ ]% [ ] % [ ]% [ ]% [ ]% [ ]% • Relationship Between Compensation Actually Paid to our PEO and the Average of the Compensation Actually Paid to the Other NEOs and the Company’s Cumulative TSR. From 2020 to 2023 , the compensation actually paid to our PEO and the average of the compensation actually paid to the Other NEOs increased by [ ]% and [ ]%, respectively, compared to a [ ]% increase in our TSR over the same time period. • Relationship Between Compensation Actually Paid to our PEO and the Average of the Compensation Actually Paid to the Other NEOs and the Company’s Net Income. From 2020 to 2023 , the compensation actually paid to our PEO and the average of the compensation actually paid to the Other NEOs increased by [ ]% and [ ]%, respectively, compared to a [ ]% increase in our Operating Income over the same time period. • Relationship Between Compensation Actually Paid to our PEO and the Average of the Compensation Actually Paid to the Other NEOs and the Company’s Adjusted EPS. From 2020 to 2023 , the compensation actually paid to our PEO and the average of the compensation actually paid to the Other NEOs increased by [ ]% and [ ]%, respectively, compared to a [ ]% increase in our Adjusted Diluted EPS over the three-year period. • Relationship Between the Company’s TSR and the Peer Group TSR . The TSR for the Peer Group disclosed in the table above increased by [ ]% from 2020 to 2023 as compared to the Company’s TSR, which increased by [ ]% over the same time period. | | | |
| Tabular List, Table | GAAP Revenue (as defined in “Compensation Discussion & Analysis—Components of Total Direct Compensation—Annual Cash Incentives”, described on page 40) Gross Margin (as defined in “Compensation Discussion & Analysis—Components of Total Direct Compensation—Annual Cash Incentives”, described on page 40 Operating Income (as defined in “Compensation Discussion & Analysis—Components of Total Direct Compensation—Annual Cash Incentives”, described on page 40) Revenue (as defined in “Compensation Discussion & Analysis—Components of Total Direct Compensation—Long-Term Incentive Awards”, described on page 42) Adjusted EPS (as defined in “Compensation Discussion & Analysis—Components of Total Direct Compensation—Long-Term Incentive Awards”, described on page 42) | | | |
| Total Shareholder Return Amount | | 104.55 | 127.77 | 98.08 |
| Peer Group Total Shareholder Return Amount | | 125.35 | 129.18 | 111.33 |
| Net Income (Loss) | | $ 245,493,000 | $ 195,423,000 | $ 67,923,000 |
| Company Selected Measure Amount | $ / shares | | 4.49 | 4.28 | 2.61 |
| PEO Name | Scott H. Baxter | Scott H. Baxter | Scott H. Baxter | Scott H. Baxter |
| Additional 402(v) Disclosure | For each year, the values included in columns (c) and (e) for the compensation actually paid to our PEO and the average compensation paid to our non-PEO NEOs reflect the following adjustments to the values included in column (b) and column (d), respectively: | | | |
| PEO | Change in Pension Value [Member] | | | | |
| Pay vs Performance Disclosure | | | | |
| Adjustment to Compensation, Amount | | $ 0 | $ 0 | $ 0 |
| PEO | Change in Stock Awards [Member] | | | | |
| Pay vs Performance Disclosure | | | | |
| Adjustment to Compensation, Amount | | (1,151,597) | 4,630,601 | (772,162) |
| PEO | Change in Option Award [Member] | | | | |
| Pay vs Performance Disclosure | | | | |
| Adjustment to Compensation, Amount | | 0 | 59,974 | (144,322) |
| Non-PEO NEO | Measure:: 1 | | | | |
| Pay vs Performance Disclosure | | | | |
| Name | GAAP Revenue | | | |
| Non-PEO NEO | Measure:: 2 | | | | |
| Pay vs Performance Disclosure | | | | |
| Name | Gross Margin | | | |
| Non-PEO NEO | Measure:: 3 | | | | |
| Pay vs Performance Disclosure | | | | |
| Name | Operating Income | | | |
| Non-PEO NEO | Measure:: 4 | | | | |
| Pay vs Performance Disclosure | | | | |
| Name | Revenue | | | |
| Non-PEO NEO | Measure:: 5 | | | | |
| Pay vs Performance Disclosure | | | | |
| Name | Adjusted EPS | | | |
| Non-PEO NEO | Change in Pension Value [Member] | | | | |
| Pay vs Performance Disclosure | | | | |
| Adjustment to Compensation, Amount | | 0 | 0 | 0 |
| Non-PEO NEO | Change in Stock Awards [Member] | | | | |
| Pay vs Performance Disclosure | | | | |
| Adjustment to Compensation, Amount | | (122,455) | 505,862 | (235,664) |
| Non-PEO NEO | Change in Option Award [Member] | | | | |
| Pay vs Performance Disclosure | | | | |
| Adjustment to Compensation, Amount | | $ 0 | $ (622) | $ (21,558) |
