Support updates and count target-sum pairs

You are given two integer arrays:

• A (fixed / primary)
• B (modifiable / secondary)

You must process a sequence of operations of two types:

1. Update : set B[index] = value .
2. Query : given an integer target , return the number of pairs (i, j) such that A[i] + B[j] == target .

Pairs are counted with multiplicity: if A contains duplicates or B contains duplicates, each index combination counts as a distinct pair.

Input

• Arrays A and B
• A list of operations, each operation is either:
  • ("update", index, value)
  • ("count", target)

Output

For each ("count", target) operation, output an integer: the number of valid pairs.

Example

• A = [1, 2, 2]
• B = [3, 2]
• Query target = 4
  • Valid pairs are (1,3) , (2,2) using the first 2 in A , and (2,2) using the second 2 in A → total 3 .

Constraints (assume typical interview constraints)

• 1 <= len(A), len(B) <= 10^5
• Number of operations up to 10^5
• Values can be negative and up to typical 32-bit integer range.