1851 - Minimum Interval to Include Each Query.

Hard

You are given a 2D integer array intervals, where <code>intervalsi = left_i, right_i</code> describes the <code>i^th</code> interval starting at <code>left_i</code> and ending at <code>right_i</code> (inclusive). The size of an interval is defined as the number of integers it contains, or more formally <code>right_i - left_i + 1</code>.

You are also given an integer array queries. The answer to the <code>j^th</code> query is the size of the smallest interval i such that <code>left_i<= queriesj<= right_i</code>. If no such interval exists, the answer is -1.

Return an array containing the answers to the queries.

Example 1:

Input: intervals = \[\[1,4],2,4,3,6,4,4], queries = 2,3,4,5

Output: 3,3,1,4

Explanation: The queries are processed as follows:

• Query = 2: The interval 2,4 is the smallest interval containing 2. The answer is 4 - 2 + 1 = 3.

• Query = 3: The interval 2,4 is the smallest interval containing 3. The answer is 4 - 2 + 1 = 3.

• Query = 4: The interval 4,4 is the smallest interval containing 4. The answer is 4 - 4 + 1 = 1.

• Query = 5: The interval 3,6 is the smallest interval containing 5. The answer is 6 - 3 + 1 = 4.

Example 2:

Input: intervals = \[\[2,3],2,5,1,8,20,25], queries = 2,19,5,22

Output: 2,-1,4,6

Explanation: The queries are processed as follows:

• Query = 2: The interval 2,3 is the smallest interval containing 2. The answer is 3 - 2 + 1 = 2.

• Query = 19: None of the intervals contain 19. The answer is -1.

• Query = 5: The interval 2,5 is the smallest interval containing 5. The answer is 5 - 2 + 1 = 4.

• Query = 22: The interval 20,25 is the smallest interval containing 22. The answer is 25 - 20 + 1 = 6.

Constraints:

• <code>1 <= intervals.length <= 10⁵</code>

• <code>1 <= queries.length <= 10⁵</code>

• intervals[i].length == 2

• <code>1 <= left_i<= right_i<= 10⁷</code>

• <code>1 <= queriesj<= 10⁷</code>