Greedy Shopping

You are given an array a_1, a_2, …, 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 ≤ i ≤ 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 ≤ n, q ≤ 2 ⋅ 10^5).

The second line contains n integers a_{1},a_{2}, …, a_{n} (1 ≤ a_{i} ≤ 10^9) — the costs of the meals. It is guaranteed, that a_1 ≥ a_2 ≥ … ≥ a_n.

Each of the next q lines contains three integers t, x, y (1 ≤ t ≤ 2, 1≤ x ≤ n, 1 ≤ y ≤ 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, …, 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.

inputFormat

Input

The first line contains two integers n, q (1 ≤ n, q ≤ 2 ⋅ 10^5).

The second line contains n integers a_{1},a_{2}, …, a_{n} (1 ≤ a_{i} ≤ 10^9) — the costs of the meals. It is guaranteed, that a_1 ≥ a_2 ≥ … ≥ a_n.

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

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

outputFormat

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, …, 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.

样例

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

8
3
6
2

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