Problem Link https://www.codechef.com/problems/ADDMUL

I wanted to understand how to handle addition and multiplication queries simultaneously. Though I read the editorial, I could not understand how to propagate lazy updates to the child nodes.

Can anyone explain me problem C ELECTRIFICATION from Educational Codeforces Round 66 (Rated for Div. 2). My doubts are from the tutorial are: 1. Since we need the dk+1 distance that means we should minimize distance to k+1 points so why we are looking over k points . 2. How they got the expression for f(x). The problem statement is https://codeforces.net/problemset/problem/1175/C and tutorial link is https://codeforces.net/blog/entry/67484