Common Permutation

This problem is from the book Programming Challenges. Here is the problem's description.

Given two strings a and b, print the longest string x of letters such that there is a
permutation of x that is a subsequence of a and there is a permutation of x that is a
subsequence of b.

Input
The input file contains several cases, each case consisting of two consecutive lines. This
means that lines 1 and 2 are a test case, lines 3 and 4 are another test case, and so on.
Each line contains one string of lowercase characters, with first line of a pair denoting
a and the second denoting b. Each string consists of at most 1,000 characters.

Output
For each set of input, output a line containing x. If several x satisfy the criteria above,
choose the first one in alphabetical order.

Sample Input
pretty
women
walking
down
the
street

Sample Output
e
nw
et

Here is my solution in C#.