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

The fund seeks to match the performance 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, hold and sell shares of the fund. You may pay other fees, such as brokerage commissions and other fees to financial intermediaries, which are not reflected in the table and examples below.

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 3.31% of the average value of its portfolio.
Portfolio Turnover, Rate rr_PortfolioTurnoverRate 3.31%
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. The examples are based on net operating expenses, which reflect the contractual undertaking by BNY Mellon Investment Adviser, Inc. 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 generally is fully invested in stocks included in the S&P 500® Index and in futures whose performance is tied to the index. The fund generally invests in all 500 stocks in the S&P 500® Index in proportion to their weighting in the 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 fees and 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. S&P 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). Companies included in the S&P 500® Index generally must have market capitalizations in excess of $13.1 billion, to the extent consistent with market conditions.

"Standard & Poor's®," "S&P®," "Standard & Poor's 500®" and "S&P 500®" are trademarks of Standard & Poor's Financial Services LLC 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 makes no 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.

● Market risk. The value of the securities in which the fund invests may be affected by political, regulatory, economic and social developments, and developments that impact specific economic sectors, industries or segments of the market.  In addition, turbulence in financial markets and reduced liquidity in equity, credit and/or fixed-income markets may negatively affect many issuers, which could adversely affect the fund.  Global economies and financial markets are becoming increasingly interconnected, and conditions and events in one country, region or financial market may adversely impact issuers in a different country, region or financial market.  These risks may be magnified if certain events or developments adversely interrupt the global supply chain; in these and other circumstances, such risks might affect companies world-wide.  Recent examples include pandemic risks related to COVID-19 and aggressive measures taken world-wide in response by governments, including closing borders, restricting international and domestic travel, and the imposition of prolonged quarantines of large populations, and by businesses, including changes to operations and reducing staff. 

● 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, 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. It is not a complete investment program.
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 shares from year to year. The table compares the average annual total returns of the fund's 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.im.bnymellon.com.
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.im.bnymellon.com
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
Q2, 2020: 20.40%

Worst Quarter
Q1, 2020: -19.74%
Highest Quarterly Return, Label rr_HighestQuarterlyReturnLabel Best Quarter
Highest Quarterly Return, Date rr_BarChartHighestQuarterlyReturnDate Jun. 30, 2020
Highest Quarterly Return rr_BarChartHighestQuarterlyReturn 20.40%
Lowest Quarterly Return, Label rr_LowestQuarterlyReturnLabel Worst Quarter
Lowest Quarterly Return, Date rr_BarChartLowestQuarterlyReturnDate Mar. 31, 2020
Lowest Quarterly Return rr_BarChartLowestQuarterlyReturn (19.74%)
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 12/31/21)
BNY Mellon S&P 500 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 28.70%
Average Annual Returns, 5 Years rr_AverageAnnualReturnYear05 18.47%
Average Annual Returns, 10 Years rr_AverageAnnualReturnYear10 16.54%
BNY Mellon S&P 500 Index Fund | BNY Mellon S&P 500 Index Fund  
Risk/Return: rr_RiskReturnAbstract  
Management fees rr_ManagementFeesOverAssets 0.25%
Shareholder services fees rr_Component1OtherExpensesOverAssets 0.25%
Miscellaneous other expenses rr_Component2OtherExpensesOverAssets 0.01%
Total other expenses rr_OtherExpensesOverAssets 0.26%
Total annual fund operating expenses rr_ExpensesOverAssets 0.51%
Fee waiver rr_FeeWaiverOrReimbursementOverAssets (0.01%) [1]
Total annual fund operating expenses (after fee waiver) rr_NetExpensesOverAssets 0.50%
Expense Example, with Redemption, 1 Year rr_ExpenseExampleYear01 $ 51
Expense Example, with Redemption, 3 Years rr_ExpenseExampleYear03 160
Expense Example, with Redemption, 5 Years rr_ExpenseExampleYear05 280
Expense Example, with Redemption, 10 Years rr_ExpenseExampleYear10 628
Expense Example, No Redemption, 1 Year rr_ExpenseExampleNoRedemptionYear01 51
Expense Example, No Redemption, 3 Years rr_ExpenseExampleNoRedemptionYear03 160
Expense Example, No Redemption, 5 Years rr_ExpenseExampleNoRedemptionYear05 280
Expense Example, No Redemption, 10 Years rr_ExpenseExampleNoRedemptionYear10 $ 628
Annual Return 2012 rr_AnnualReturn2012 15.45%
Annual Return 2013 rr_AnnualReturn2013 31.76%
Annual Return 2014 rr_AnnualReturn2014 13.15%
Annual Return 2015 rr_AnnualReturn2015 0.91%
Annual Return 2016 rr_AnnualReturn2016 11.35%
Annual Return 2017 rr_AnnualReturn2017 21.26%
Annual Return 2018 rr_AnnualReturn2018 (4.88%)
Annual Return 2019 rr_AnnualReturn2019 30.87%
Annual Return 2020 rr_AnnualReturn2020 17.77%
Annual Return 2021 rr_AnnualReturn2021 28.08%
Average Annual Returns, 1 Year rr_AverageAnnualReturnYear01 28.08%
Average Annual Returns, 5 Years rr_AverageAnnualReturnYear05 17.89%
Average Annual Returns, 10 Years rr_AverageAnnualReturnYear10 15.98%
BNY Mellon S&P 500 Index Fund | BNY Mellon S&P 500 Index Fund | After Taxes on Distributions  
Risk/Return: rr_RiskReturnAbstract  
Average Annual Returns, 1 Year rr_AverageAnnualReturnYear01 24.55%
Average Annual Returns, 5 Years rr_AverageAnnualReturnYear05 14.64%
Average Annual Returns, 10 Years rr_AverageAnnualReturnYear10 13.58%
BNY Mellon S&P 500 Index Fund | BNY Mellon S&P 500 Index Fund | After Taxes on Distributions and Sale of Fund Shares  
Risk/Return: rr_RiskReturnAbstract  
Average Annual Returns, 1 Year rr_AverageAnnualReturnYear01 19.07%
Average Annual Returns, 5 Years rr_AverageAnnualReturnYear05 13.70%
Average Annual Returns, 10 Years rr_AverageAnnualReturnYear10 12.78%
[1] The fund's investment adviser, BNY Mellon Investment Adviser, Inc., has agreed in its management agreement with the fund to: (1) pay all of the fund's expenses, except management fees, shareholder services plan fees and certain other expenses, including the fees and expenses of the non-interested board members and the fees and expenses of counsel to the fund and to the non-interested board members, and (2) reduce its fee pursuant to the management agreement in an amount equal to the fund's allocable portion of the fees and expenses of the non-interested board members and the fees and expenses of counsel to the fund and to the non-interested board members (in the amount of .01% for the past fiscal year). These provisions in the management agreement may not be amended without the approval of the fund's shareholders.