Distinct Moves

Problem Overview

• Core task: In this coding interview problem, count subsequences of a move string that take you from x to y on a number line 0..n.
• I/O: s with 'l'/'r' moves; integers n, x, y; return the number of valid subsequences modulo 1e9+7.
• Constraints: 1<=|s|<=1e3; 0<=x,y,n<=2500.
• Context: Discrete path counting for movement on a number line (navigation/domain modeling).
• Source: Asked in Flexport interviews; a common interview question from Flexport.