Given two non-empty strings A and B composed of lowercase Latin letters, what is the minimum number of substrings of A needed to form string B? The lengths of A and B are at most 100000. If the task is not possible for a given input, output a rogue value (a.k.a. -1).

I was thinking about solving this with an O(N^2) DP, but that does not fit into the time limit of 5 seconds.

Please help, and thanks in advance!

EDIT: Note that chosen substrings can overlap. I put some cases below.

Input 1: abcbcd abcd

Output 1: 2

Input 2: iamsmart iamdumb

Output 2: -1

Input 3: asmallmallinmalta atallmallinlima

Output 3: 5

Explanations: "abcd" = "ab" + "cd", no "d"s in the first string of Input 2, "atallmallinlima" = "a" + "ta" + "llmallin" + "li" + "ma"