Sum of Subarray Minimums

Count each element's contribution as the minimum rather than enumerating subarrays. For index i, let L be the distance to the previous strictly smaller element and R the distance to the next smaller-or-equal element, or use the opposite strictness consistently. Then nums[i] is selected as minimum for exactly L*R subarrays, contributing nums[i]*L*R. Compute boundaries with monotonic increasing stacks of indices. The asymmetric strictness is essential for duplicates: if both sides use the same strict comparison, equal values are double-counted or missed. Accumulate with a wide integer and apply the specified modulo safely. Each index is pushed and popped at most once, so time is O(n) and extra space is O(n). Explain the endpoint-choice proof: any start between the left boundary and i and any end between i and the right boundary yields a subarray assigned to i.