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Google Sheets: Sum till particular date

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I have time-series data that follows no predictable entries. For example as below.

DateUnits
01 Jan 20221
05 Jan 20222
08 Jan 20221
30 Jan 20221
04 Feb 20221
10 Feb 20221
13 Feb 20222
28 Feb 20221
07 Mar 20223
14 Mar 20221
23 Mar 20221
28 Mar 20223

What I want to do here is I want to add a sum to particular date. Expected output looks something below this.

DateTotal Units till that date
01 Jan 2022?
15 Jan 2022?
01 Feb 2022?
15 Feb 2022?
01 Mar 2022?
15 Mar 2022?

Now, I don't want to add all the dummy entries for missing dates in input table (because data is going to be huge)

Is there any way I can create a summary like this?


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