Suppose you have coins of values $1,3$ and $4.$ You use a greedy algorithm, in which you choose the largest value coin which is not greater than the remaining sum. For which of the following sums, will the algorithm produce an optimal answer?

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a$.$

$14$ and $20$

b$.$

$20$

c$.$

$10$

d$.$

$14$

e$.$

none