You are given an integer array nums and an integer k.

In one operation, you can increase or decrease any element of nums by exactly k.

You are also given a 2D integer array queries, where each queries[i] = [l_i, r_i].

For each query, find the minimum number of operations required to make all elements in the subarray nums[l_i..r_i] equal. If it is impossible, the answer for that query is -1.

Return an array ans, where ans[i] is the answer for the i^th query.

Example 1:

Input: nums = [1,4,7], k = 3, queries = [[0,1],[0,2]]

Output: [1,2]

Explanation:

One optimal set of operations:

`i`	`[l_i, r_i]`	`nums[l_i..r_i]`	Possibility	Operations	Final `nums[l_i..r_i]`	`ans[i]`
0	[0, 1]	[1, 4]	Yes	`nums[0] + k = 1 + 3 = 4 = nums[1]`	[4, 4]	1
1	[0, 2]	[1, 4, 7]	Yes	`nums[0] + k = 1 + 3 = 4 = nums[1] nums[2] - k = 7 - 3 = 4 = nums[1]`	[4, 4, 4]	2

Thus, ans = [1, 2].

Example 2:

Input: nums = [1,2,4], k = 2, queries = [[0,2],[0,0],[1,2]]

Output: [-1,0,1]

Explanation:

One optimal set of operations:

`i`	`[l_i, r_i]`	`nums[l_i..r_i]`	Possibility	Operations	Final `nums[l_i..r_i]`	`ans[i]`
0	[0, 2]	[1, 2, 4]	No	-	[1, 2, 4]	-1
1	[0, 0]	[1]	Yes	Already equal	[1]	0
2	[1, 2]	[2, 4]	Yes	`nums[1] + k = 2 + 2 = 4 = nums[2]`	[4, 4]	1

Thus, ans = [-1, 0, 1].

Constraints:

1 <= n == nums.length <= 4 × 10⁴
1 <= nums[i] <= 10⁹
1 <= k <= 10⁹
1 <= queries.length <= 4 × 10⁴
queries[i] = [l_i, r_i]
0 <= l_i <= r_i <= n - 1