CCC '01 S5 - Post's Correspondence Problem

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Points: 10 (partial)
Time limit: 1.0s
Memory limit: 256M
Problem types
Canadian Computing Competition: 2001 Stage 1, Senior #5

Let A and B be two sequences of non-empty strings:

\displaystyle \begin{align*} A &= (a_1, a_2, \dots, a_n) \\ B &= (b_1, b_2, \dots, b_n) \end{align*}

Let m be a positive integer. Does there exist a sequence of integers i_1, i_2, \dots, i_k such that m > k > 0 and a_{i_1} a_{i_2} \dots a_{i_k} = b_{i_1} b_{i_2} \dots b_{i_k}?

For example, if A = (a, abaaa, ab) and B = (aaa, ab, b), then the required sequence of integers is (2, 1, 1, 3) giving abaaaaaab = abaaaaaab.

Input Specification

The first two lines of input will contain m and n respectively, and m \times n \le 40. The next 2n lines contain in order the elements of A followed by the elements of B. Each string is at most 20 characters.

Output Specification

If a solution exists, print k on a line by itself, followed by the integer sequence in order, one element per line. Otherwise, print a single line containing No solution..

Sample Input 1

7
3
a
abaaa
ab
aaa
ab
b

Sample Output 1

4
2
1
1
3

Sample Input 2

10
3
abc
def
ghi
bcd
efg
hia

Sample Output 2

No solution.

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