def paths_with_obstacles(grid):
    if not grid or not grid[0]:
        return 0
    dp = [0] * len(grid[0])
    dp[0] = 1
    for row in grid:
        for c, blocked in enumerate(row):
            if blocked:
                dp[c] = 0
            elif c:
                dp[c] += dp[c - 1]
    return dp[-1]