Answer parity-alternation range queries

You are given an integer array nums of length n and q queries. Each query is a pair [l, r] (0-indexed, inclusive).

A subarray nums[l..r] is called alternating-parity if for every index i with l < i <= r, nums[i] and nums[i-1] have different parity (one even, one odd).

For each query [l, r], determine whether nums[l..r] is alternating-parity.

Input

• nums : array of integers
• queries : list of [l, r]

Output

• An array of booleans ans , where ans[j] corresponds to query queries[j] .

Constraints (typical)

• 1 <= n, q <= 2*10^5
• 0 <= l <= r < n
• |nums[i]| <= 10^9

Goal: answer all queries efficiently (faster than checking each subarray element-by-element per query).