You are given an integer array nums and a list of operations queries, where each operation queries[i] = [l_i, r_i, val_i].

For a fixed integer k, apply the first k operations in order. When applying an operation [l_i, r_i, val_i], you may choose for every index j in the range l_i to r_i an integer decrement d_j such that $0 \leq d_j \leq val_i$, and then update nums[j] = nums[j] - d_j.

After applying the first k operations, the array is called a zero array if every element is equal to $0$.

Return the minimum k such that it is possible to make nums a zero array after applying the first k operations. If it is impossible for any k, return $-1$.

Note: In each operation, the decrement chosen at each index can be different, but it must be between $0$ and val_i inclusive.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $0 \leq$ nums[i] $\leq 5 \cdot 10^5$

• $1 \leq$ queries.length $\leq 10^5$

• queries[i].length $= 3$

• $0 \leq$ l_i $\leq$ r_i $<$ nums.length

• $1 \leq$ val_i $\leq 5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.