How To Find Corresponding Values Spread Across Different Columns

I have a workbook with two sheets, and I am having difficulty in finding how to match up the data.

Sheet 1 (named "TS") consists of several columns, but it's always a series of date columns followed by multiple site numbers.

Sheet 2 (named "Dates") consists of just two columns, a site ID and a Date column.

I am having difficulty in finding how to lookup/match the date that goes with the store number, as the information in Sheet 1 (TS) is laid out in a horizontal fashion.

So, for example:
Sites: 14352, 14425, 11661, 404, 8142, 3571 should all have the date of 5/17/2014.

As such, on Sheet 2 (Dates), whenever those site IDs are encountered, the date of 5/17/2014 would need to be applied in col B.

Similarly, on Sheet 2 (Dates), for site IDs 1201, 3613, 9316, 9735, 13211, 7640, the date of 6/21/2014 would need to be applied in col B.

Here is a link to a sample workbook: [URL] ........