Hi! Could anyone help me with this discrete math question? Thank you so much!

3 Secret Veto In the usual secret-sharing scenario we consider (for instance) a secret vault at the United Nations, which we want to design with the property that any k representatives can pool their information and open it, but any smaller number has no hope of doing so. Assume that the solution in the notes has been implemented, so that the key is some number s, and each member has been assigned a number f (1) mod q for some degree k 1 polynomial f with coefcients in GF(q) and satisfying f(0) = s. (a) A group of k + E representatives get together to discuss opening the vault. What will happen if E representatives are opposed to opening the vault and, instead of revealing their true numbers, secretly reveal some diferent numbers from GF(q)? Will the group be able to open the vault? If so, how long will it take? (b) Repeat part (a) in the event that only E / 2 of the E representatives in opposition reveal different numbers than they were assignedassume that E is even