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Reconciliation of Weighted Average Common Shares Outstanding Used for Computation of Basic and Diluted Net Income per Common Share (Detail) - shares	12 Months Ended
	Jan. 31, 2021	Jan. 31, 2020	Jan. 31, 2019
Earnings Per Share [Abstract]
Basic weighted-average common shares outstanding	97,817,651	99,833,011	108,303,594
Effect of dilutive options, stock appreciation rights, restricted stock units and performance stock units	705,125	755,666	1,402,413
Diluted weighted-average shares outstanding	98,522,776	100,588,677	109,706,007

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- Definition

Additional shares included in the calculation of diluted EPS as a result of the potentially dilutive effect of share based payment arrangements using the treasury stock method.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 45
-Paragraph 22
-URI http://asc.fasb.org/extlink&oid=121326447&loc=d3e1707-109256

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=6371337&loc=d3e3550-109257

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 45
-Paragraph 28A
-URI http://asc.fasb.org/extlink&oid=121326447&loc=d3e1500-109256

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
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-Section 45
-Paragraph 23
-Subparagraph (c)
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- Definition

The average number of shares or units issued and outstanding that are used in calculating diluted EPS or earnings per unit (EPU), determined based on the timing of issuance of shares or units in the period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=6371337&loc=d3e3550-109257

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 45
-Paragraph 16
-URI http://asc.fasb.org/extlink&oid=121326447&loc=d3e1505-109256

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Number of [basic] shares or units, after adjustment for contingently issuable shares or units and other shares or units not deemed outstanding, determined by relating the portion of time within a reporting period that common shares or units have been outstanding to the total time in that period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=6371337&loc=d3e3550-109257

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 45
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=121326447&loc=d3e1448-109256

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