CF1439C.Greedy Shopping

You are given an array $a_1, a_2, \ldots, a_n$ of integers. This array is non-increasing.

Let's consider a line with $n$ shops. The shops are numbered with integers from $1$ to $n$ from left to right. The cost of a meal in the $i$ -th shop is equal to $a_i$ .

You should process $q$ queries of two types:

• 1 x y: for each shop $1 \leq i \leq x$ set $a_{i} = max(a_{i}, y)$ .
• 2 x y: let's consider a hungry man with $y$ money. He visits the shops from $x$ -th shop to $n$ -th and if he can buy a meal in the current shop he buys one item of it. Find how many meals he will purchase. The man can buy a meal in the shop $i$ if he has at least $a_i$ money, and after it his money decreases by $a_i$ .

The first line contains two integers $n$ , $q$ ( $1 \leq n, q \leq 2 \cdot 10^5$ ).

The second line contains $n$ integers $a_{1},a_{2}, \ldots, a_{n}$ $(1 \leq a_{i} \leq 10^9)$ — the costs of the meals. It is guaranteed, that $a_1 \geq a_2 \geq \ldots \geq a_n$ .

Each of the next $q$ lines contains three integers $t$ , $x$ , $y$ ( $1 \leq t \leq 2$ , $1\leq x \leq n$ , $1 \leq y \leq 10^9$ ), each describing the next query.

It is guaranteed that there exists at least one query of type $2$ .

For each query of type $2$ output the answer on the new line.

In the first query a hungry man will buy meals in all shops from $3$ to $10$ .

In the second query a hungry man will buy meals in shops $4$ , $9$ , and $10$ .

After the third query the array $a_1, a_2, \ldots, a_n$ of costs won't change and will be $\{10, 10, 10, 6, 6, 5, 5, 5, 3, 1\}$ .

In the fourth query a hungry man will buy meals in shops $2$ , $3$ , $4$ , $5$ , $9$ , and $10$ .

After the fifth query the array $a$ of costs will be $\{10, 10, 10, 7, 6, 5, 5, 5, 3, 1\}$ .

In the sixth query a hungry man will buy meals in shops $2$ and $4$ .