Dynamic Path Solution

function add(u, v, x)
    makeRoot(u)
    access(v)
    // Path u-v is v's auxiliary tree
    v.lazy := v.lazy + x
    // Don't pushDown yet - lazy stays until needed

function query(u, v)
    makeRoot(u)
    access(v)
    return v.subtreeSum

Remember to:

• Push down lazy before accessing children
• Push up sums after rotations
• Handle reversal flag correctly with lazy add

The combination of reversal and lazy add requires careful ordering in pushDown.