Consider a Floating-Strike Lookback Put Option Written on a Stock $S ^ { \mathrm { max } }$

Consider a floating-strike lookback put option written on a stock.Let $S ^ { \mathrm { max } }$ and $S ^ { \mathrm { min } }$ denote the maximum and minimum prices of the stock over the option's life.Then,the payoff to the option holder is given by $\max \{ X - Y , 0 \}$ ,where

A) $X = S ^ { \max }$
And
$Y = K$
,the given strike price of the option.
B) $X = K$
And
$Y = S ^ { \text {min } }$
)
C) $X = S ^ { \max }$
And
$Y = S _ { T }$
,the price of the underlying at maturity.
D) $X = S _ { T }$
And
$Y = S ^ { \text {min } }$
)