k (minimum number of queries), and use binary search over k.

For every k, check whether the first k queries can reduce nums to a Zero Array:

Use a difference array to efficiently apply the range updates defined by the first k queries.
Simulate the cumulative effects of the difference array on nums and verify if all elements become ≤ 0.

If nums can be zeroed with k queries, explore smaller values of k (move left in binary search). Otherwise, move right to try larger k.

Return the smallest valid k, or