The correlation and competition between antiferromagnetism and superconductivity are one of the most fundamental issues in high temperature superconductors. Superconductivity in high temperature cuprate superconductors arises from suppressing an antiferromagnetic (AFM) Mott insulator while in iron-pnictide superconductors arises from AFM semimetals and can coexist with AFM orders. This difference raises many intriguing debates on the relation between the two classes of high temperature superconductors. Recently, superconductivity at 32 K has been reported in iron-chalcogenide superconductors A_xFe_2−ySe₂ (A = K, Rb, and Cs). They have the same structure as that of iron-pnictide 122-system. Here, we report electronic and magnetic phase diagram of K_xFe_2−ySe₂ system as a function of Fe valence. We find a superconducting phase sandwiched between two AFM insulating phases. The two insulating phases are characterized by two distinct superstructures caused by Fe vacancy orders with modulation wave vectors of q₁ = (1/5, 3/5, 0) and q₂ = (1/4, 3/4, 0), respectively.

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