C. Greedy Shopping
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$a_i$$$.
Input

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 $$$2$$$.

Output

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

Example
Input
10 6
10 10 10 6 6 5 5 5 3 1
2 3 50
2 4 10
1 3 10
2 2 36
1 4 7
2 2 17
Output
8
3
6
2
Note

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 $$$4$$$.