Distinct Number Line Moves

You are given a number line with positions labeled from 0 to n, a string s of move instructions, and two positions x and y.

A move instruction 'l' moves one step left, and 'r' moves one step right. You may choose any subsequence of s, preserving order, and execute that subsequence starting from position x. The position must always remain between 0 and n.

Two subsequences are considered the same if their resulting move strings are identical, even if they came from different indices of s.

Return the number of distinct subsequence move strings that take you from x to y, modulo 1_000_000_007.