Problem on Queries

I have an array A of N elements (1 <= N <= 200000). Now I have Q (1 <= Q <= 200000) queries. In each query, 3 integers x, l and r are given. I have to find min{x*j + A[j]} where l <= j <= r. I was thinking about solving this by segment tree or dynamic programming but still I can’t handle proper time complexity.
Example: Input Array A = [12, 13, 33, 25, 10, 41, 51, 2].
Query: 2 1 5 Output: 14
Query: 5 5 8 Output: 35.
Can anybody tell me the right approach?

segment tree,having convex hull trick in each node

See july long challenge’s pdeliv editorial…

thank you bro…

//