My Biology book says the lack of vitamin K lets people problems in coagulation. Could you tell me exactly why

Why do people that don't ingest enough vitamin K don't have a good coagulation? Where/How does vitamin K act in the process of coagulation?

Vitamin K is involved in the carboxylation of certain glutamate residues in proteins to form gamma-carboxyglutamate (Gla) residues. The modified residues are oftensituated within specific protein domains called Gla domains. Gla residues are usually involved in binding calcium, and are essential for the biological activity of all known Gla proteins

15 human proteins with Gla domains have been discovered, and they play key roles in the regulation of three physiological processes:

Blood coagulation: prothrombin (factor II), factors VII, IX, and X, and proteins C