Coin Queue

You need to maintain a queue that is initially empty. You will perform three types of operations on the queue -

1 X - Add the number x to the queue.

2 0 - Remove the least recently added number from the queue.

3 X - Consider the current numbers in the queue. Find the maximum size of a subset of numbers in the queue whose sum is X. If there is no such subset, return -1.

A subset is defined as a sequence that can be obtained by removing some (possibly all) elements present in the queue.

1 <= X <= 350

|A| <= 10⁵

Input 1:

  A : 
  [
    [1, 3]
    [1, 1]
    [1, 1]
    [2, 0]
    [3, 2]
  ]

Input 2:

  A : 
  [
    [1, 1]
    [1, 2]
    [1, 2]
    [1, 3]
    [3, 4]
    [3, 5]
  ]

Output 1:

  [2]

Output 2:

  [2, 3]

Explanation 1:

  After first 3 operations, queue becomes {3, 1, 1}.
  Then we pop the number 3. The queue is {1, 1}.
  Then we can form 2 by taking both the ones. So, we have a subset of 2 numbers.

Explanation 2:

  After first 3 operations, queue becomes {1, 2, 2, 3}.
  Then 4 can be formed by 2 + 2 and 1 + 3. Max 2 numbers are in a subset.
  5 can be formed by 1 + 2 + 2, 2 + 3 and 2 + 3. Max 3 numbers are in a subset.