Number of Ways to Reach Destination in the Grid

Count the number of distinct ways to go from the top-left to the bottom-right of a grid under given movement constraints (e.g., obstacles or variable step lengths per cell), returning the result modulo 1e9+7; the challenge is to handle large grids and exponential branching by using optimized DP/graph techniques (prefix sums, memoization, or DAG reasoning) to avoid naive O(n^3) work.