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BNY Mellon Institutional S&P 500 Stock Index Fund  
Risk/Return: rr_RiskReturnAbstract  
Risk/Return [Heading] rr_RiskReturnHeading Fund Summary
Objective [Heading] rr_ObjectiveHeading Investment Objective
Objective, Primary [Text Block] rr_ObjectivePrimaryTextBlock

The fund seeks to match the total return of the S&P 500® Index.
Expense [Heading] rr_ExpenseHeading Fees and Expenses
Expense Narrative [Text Block] rr_ExpenseNarrativeTextBlock

This table describes the fees and expenses that you may pay if you buy and hold shares of the fund.
Operating Expenses Caption [Text] rr_OperatingExpensesCaption Annual Fund Operating Expenses (expenses that you pay each year as a percentage of the value of your investment)
Portfolio Turnover [Heading] rr_PortfolioTurnoverHeading Portfolio Turnover
Portfolio Turnover [Text Block] rr_PortfolioTurnoverTextBlock

The fund pays transaction costs, such as commissions, when it buys and sells securities (or "turns over" its portfolio). A higher portfolio turnover may indicate higher transaction costs and may result in higher taxes when fund shares are held in a taxable account. These costs, which are not reflected in annual fund operating expenses or in the Example, affect the fund's performance. During the most recent fiscal year, the fund's portfolio turnover rate was 4.53% of the average value of its portfolio.
Portfolio Turnover, Rate rr_PortfolioTurnoverRate 4.53%
Expense Example [Heading] rr_ExpenseExampleHeading Example
Expense Example Narrative [Text Block] rr_ExpenseExampleNarrativeTextBlock

The Example is intended to help you compare the cost of investing in the fund with the cost of investing in other mutual funds. The Example assumes that you invest $10,000 in the fund for the time periods indicated and then hold or redeem all of your shares at the end of those periods. The Example also assumes that your investment has a 5% return each year and that the fund's operating expenses remain the same. Although your actual costs may be higher or lower, based on these assumptions your costs would be:
Strategy [Heading] rr_StrategyHeading Principal Investment Strategy
Strategy Narrative [Text Block] rr_StrategyNarrativeTextBlock

To pursue its goal, the fund normally invests at least 95% of its total assets in common stocks included in the S&P 500® Index. To replicate index performance, the fund's portfolio managers use a passive management approach and generally purchase all of the securities comprising the S&P 500® Index (though, at times, the fund may invest in a representative sample of the S&P 500® Index). Because the fund has expenses, performance will tend to be slightly lower than that of the S&P 500® Index. The fund attempts to have a correlation between its performance and that of the S&P 500® Index of at least .95, before expenses. A correlation of 1.00 would mean that the fund and the index were perfectly correlated.


The S&P 500® Index is an unmanaged index of 500 common stocks chosen to reflect the industries of the U.S. economy and is often considered a proxy for the stock market in general. Companies included in the S&P 500® Index generally must have market capitalizations in excess of $8.2 billion, to the extent consistent with market conditions. Standard & Poor's weights each company's stock in the index by its market capitalization (i.e., the share price times the number of shares outstanding), adjusted by the number of available float shares (i.e., those shares available to public investors).


"Standard & Poor's®," "S&P®," "Standard & Poor's 500™," and "S&P 500®," are trademarks of Standard & Poor's Financial Services, LLC (Standard & Poor's), and have been licensed for use by the fund. The fund is not sponsored, endorsed, sold or promoted by Standard & Poor's, and Standard & Poor's does not make any representation regarding the advisability of investing in the fund.
Risk [Heading] rr_RiskHeading Principal Risks
Risk Narrative [Text Block] rr_RiskNarrativeTextBlock

An investment in the fund is not a bank deposit. It is not insured or guaranteed by the Federal Deposit Insurance Corporation (FDIC) or any other government agency. It is not a complete investment program. The fund's share price fluctuates, sometimes dramatically, which means you could lose money.


· Risks of stock investing. Stocks generally fluctuate more in value than bonds and may decline significantly over short time periods. There is the chance that stock prices overall will decline because stock markets tend to move in cycles, with periods of rising prices and falling prices. The market value of a stock may decline due to general market conditions or because of factors that affect the particular company or the company's industry.


· Indexing strategy risk. The fund uses an indexing strategy. It does not attempt to manage market volatility, use defensive strategies or reduce the effects of any long-term periods of poor index performance. The correlation between fund and index performance may be affected by the fund's expenses and use of sampling techniques, changes in securities markets, changes in the composition of the index and the timing of purchases and redemptions of fund shares.
Risk Lose Money [Text] rr_RiskLoseMoney The fund's share price fluctuates, sometimes dramatically, which means you could lose money.
Risk Not Insured Depository Institution [Text] rr_RiskNotInsuredDepositoryInstitution An investment in the fund is not a bank deposit. It is not insured or guaranteed by the Federal Deposit Insurance Corporation (FDIC) or any other government agency.
Bar Chart and Performance Table [Heading] rr_BarChartAndPerformanceTableHeading Performance
Performance Narrative [Text Block] rr_PerformanceNarrativeTextBlock

The following bar chart and table provide some indication of the risks of investing in the fund. The bar chart shows changes in the performance of the fund's Class I shares from year to year. The table compares the average annual total returns of the fund's Class I shares to those of a broad measure of market performance. The fund's past performance (before and after taxes) is not necessarily an indication of how the fund will perform in the future. More recent performance information may be available at www.bnymellonim.com/us. Prior to August 31, 2016, the fund's Class I shares were undesignated.

Performance Information Illustrates Variability of Returns [Text] rr_PerformanceInformationIllustratesVariabilityOfReturns The following bar chart and table provide some indication of the risks of investing in the fund.
Performance Availability Website Address [Text] rr_PerformanceAvailabilityWebSiteAddress www.bnymellonim.com/us
Performance Past Does Not Indicate Future [Text] rr_PerformancePastDoesNotIndicateFuture The fund's past performance (before and after taxes) is not necessarily an indication of how the fund will perform in the future.
Bar Chart [Heading] rr_BarChartHeading Year-by-Year Total Returns as of 12/31 each year (%)
Bar Chart Closing [Text Block] rr_BarChartClosingTextBlock

Best Quarter
Q1, 2019: 13.62%
Worst Quarter
Q3, 2011: -13.90%
Highest Quarterly Return, Label rr_HighestQuarterlyReturnLabel Best Quarter
Highest Quarterly Return, Date rr_BarChartHighestQuarterlyReturnDate Mar. 31, 2019
Highest Quarterly Return rr_BarChartHighestQuarterlyReturn 13.62%
Lowest Quarterly Return, Label rr_LowestQuarterlyReturnLabel Worst Quarter
Lowest Quarterly Return, Date rr_BarChartLowestQuarterlyReturnDate Sep. 30, 2011
Lowest Quarterly Return rr_BarChartLowestQuarterlyReturn (13.90%)
Index No Deduction for Fees, Expenses, Taxes [Text] rr_IndexNoDeductionForFeesExpensesTaxes reflects no deductions for fees, expenses or taxes
Performance Table Uses Highest Federal Rate rr_PerformanceTableUsesHighestFederalRate After-tax returns are calculated using the historical highest individual federal marginal income tax rates, and do not reflect the impact of state and local taxes.
Performance Table Not Relevant to Tax Deferred rr_PerformanceTableNotRelevantToTaxDeferred Actual after-tax returns depend on the investor's tax situation and may differ from those shown, and the after-tax returns shown are not relevant to investors who hold their shares through U.S. tax-deferred arrangements such as 401(k) plans or individual retirement accounts.
Performance Table Narrative rr_PerformanceTableNarrativeTextBlock

After-tax returns are calculated using the historical highest individual federal marginal income tax rates, and do not reflect the impact of state and local taxes. Actual after-tax returns depend on the investor's tax situation and may differ from those shown, and the after-tax returns shown are not relevant to investors who hold their shares through U.S. tax-deferred arrangements such as 401(k) plans or individual retirement accounts.

Average Annual Return, Caption rr_AverageAnnualReturnCaption Average Annual Total Returns (as of 12/31/19)
BNY Mellon Institutional S&P 500 Stock Index Fund | S&P 500® Index reflects no deductions for fees, expenses or taxes  
Risk/Return: rr_RiskReturnAbstract  
Average Annual Returns, 1 Year rr_AverageAnnualReturnYear01 31.46%
Average Annual Returns, 5 Years rr_AverageAnnualReturnYear05 11.69%
Average Annual Returns, 10 Years rr_AverageAnnualReturnYear10 13.55%
BNY Mellon Institutional S&P 500 Stock Index Fund | Class I  
Risk/Return: rr_RiskReturnAbstract  
Management fees rr_ManagementFeesOverAssets 0.20%
Other expenses rr_OtherExpensesOverAssets 0.01%
Total annual fund operating expenses rr_ExpensesOverAssets 0.21%
Fee waiver rr_FeeWaiverOrReimbursementOverAssets (0.01%) [1]
Total annual fund operating expenses (after fee waiver) rr_NetExpensesOverAssets 0.20%
Expense Example, with Redemption, 1 Year rr_ExpenseExampleYear01 $ 20
Expense Example, with Redemption, 3 Years rr_ExpenseExampleYear03 64
Expense Example, with Redemption, 5 Years rr_ExpenseExampleYear05 113
Expense Example, with Redemption, 10 Years rr_ExpenseExampleYear10 255
Expense Example, No Redemption, 1 Year rr_ExpenseExampleNoRedemptionYear01 20
Expense Example, No Redemption, 3 Years rr_ExpenseExampleNoRedemptionYear03 64
Expense Example, No Redemption, 5 Years rr_ExpenseExampleNoRedemptionYear05 113
Expense Example, No Redemption, 10 Years rr_ExpenseExampleNoRedemptionYear10 $ 255
Annual Return 2010 rr_AnnualReturn2010 14.93%
Annual Return 2011 rr_AnnualReturn2011 1.98%
Annual Return 2012 rr_AnnualReturn2012 15.79%
Annual Return 2013 rr_AnnualReturn2013 32.18%
Annual Return 2014 rr_AnnualReturn2014 13.45%
Annual Return 2015 rr_AnnualReturn2015 1.20%
Annual Return 2016 rr_AnnualReturn2016 11.74%
Annual Return 2017 rr_AnnualReturn2017 21.58%
Annual Return 2018 rr_AnnualReturn2018 (4.59%)
Annual Return 2019 rr_AnnualReturn2019 31.29%
Average Annual Returns, 1 Year rr_AverageAnnualReturnYear01 31.29%
Average Annual Returns, 5 Years rr_AverageAnnualReturnYear05 11.49%
Average Annual Returns, 10 Years rr_AverageAnnualReturnYear10 13.36%
BNY Mellon Institutional S&P 500 Stock Index Fund | Class I | After Taxes on Distributions  
Risk/Return: rr_RiskReturnAbstract  
Average Annual Returns, 1 Year rr_AverageAnnualReturnYear01 29.75%
Average Annual Returns, 5 Years rr_AverageAnnualReturnYear05 10.47%
Average Annual Returns, 10 Years rr_AverageAnnualReturnYear10 12.65%
BNY Mellon Institutional S&P 500 Stock Index Fund | Class I | After Taxes on Distributions and Sale of Fund Shares  
Risk/Return: rr_RiskReturnAbstract  
Average Annual Returns, 1 Year rr_AverageAnnualReturnYear01 19.57%
Average Annual Returns, 5 Years rr_AverageAnnualReturnYear05 8.98%
Average Annual Returns, 10 Years rr_AverageAnnualReturnYear10 11.09%
[1] The fund's investment adviser, BNY Mellon Investment Adviser, Inc., has agreed in its investment management agreement with the fund to: (1) pay all of the fund's expenses, except management fees and certain other expenses, including the fees and expenses of the non-interested board members and their counsel, and (2) reduce its fees pursuant to the investment management agreement in an amount equal to the fund's allocable portion of the fees and expenses of the non-interested board members and their counsel (in the amount of .01% for the past fiscal year). These provisions in the investment management agreement may not be amended without the approval of the fund's shareholders.