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To use GLK 22 40S&W 31RD you need Kel-tec that takes glock .40 magazines
You will need this for the particular firearm you mention. https://www.budsgunshop.com/catalog/product_info.php/products_id/24034/Smith+%26+Wesson+3007346+S%26W+M%26P+40+Smith+%26+Wesson+%28S%26W%29+15+rd+Steel+Black+Body%2FF --- Or if you need more capacity this : https://www.budsgunshop.com/catalog/product_info.php/products_id/89682/ProMag+SMI-A13+S%26W+M%26P40+Magazine+25RD+40S%26W+Blued+Steel
The model you have pictured above will work with these mags, but the one you typed out will not. Kel-tec has many configurations as you probably knew, where you can mix and match. But here one is setup for S&W M&P mags, the other for Glock mags. They put out a list somewhere online, and Hickcock45 has a YouTube video that names all (or most) setups.