(B) any other contract that may require or involve the employment of laborers or mechanics if the contract is one
(i) to which the Government, an agency or instrumentality of the Government, a territory, or the District of Columbia is a party;
(ii) which is made for or on behalf of the Government, an agency or instrumentality, a territory, or the District of Columbia; or
(iii) which is a contract for work financed at least in part by loans or grants from, or loans insured or guaranteed by, the Government or an agency or instrumentality under any federal law providing wage standards for the work.