When data is transmitted across a noisy channel, information can be lost during the transmission. For example, a message that is sent through a noisy channel as 

“WHO PARKED ON HARRY POTTER’S SPOT? 

could be received as the message, 

“HOP ON POP''

That is, some characters could be lost during the transmission, so that only a selected portion of the original message is received. We can model this phenomenon using character strings, where, given a string X = x₁x₂ ...x_n, we say that a string Y = y₁y₂ ...y_m is a subsequence of X if there are a set of indices {i₁, i₂,...,i_k}, such that y₁ = x_i1 , y₂ = x_i2 , ..., y_k = x_ik , and i_j < i_j+1, for j = 1, 2,...,k − 1. In a case of transmission along a noisy channel, it could be useful to know if our transcription of a received message is indeed a subsequence of the message sent. Therefore, describe an O(n + m)-time method for determining if a given string, Y , of length m is a subsequence of a given string, X, of length n.