n users have shared two secrets using Shamir secret sharing. User i has a share s; = (i, yi) of the secret m, and a share si = (i, y) of the secret m'. Both sets of shares use the same prime modulus p. Suppose each user i locally computes zi = (y + y) % p. (a) Prove that if the shares of m and shares of m' had the same threshold, then the resulting {(i, z) | i n} are a valid secret-sharing of the secret m + m'. (b) Describe what the users get when the shares of m and m' had different thresholds (say, t and t', respectively).