Ga. (10 points) for i ∈ {1, . . , k}, n ∈ n, and b ∈ {0, 1}, let c(i, n, b) denote the number of cursed coins needed to make n cents in change using only the last i denominations dk−i+1, dk−i+2, . . , dk, where dk−i+2 is allowed to be used if and only if i ≤ 2 or b = 0. that is, b is a boolean “flag” variable indicating whether we are excluding the next denomination dk−i+2 or not (b = 1 means exclude it).write down a recurrence relation for c and prove it is correct. be sure to include the base case.