DZY Loves Fibonacci Numbers

4000ms

262144K

Description:

In mathematical terms, the sequence F_n of Fibonacci numbers is defined by the recurrence relation

F₁ = 1; F₂ = 1; F_n = F_n - 1 + F_n - 2 (n > 2).

DZY loves Fibonacci numbers very much. Today DZY gives you an array consisting of n integers: a₁, a₂, ..., a_n. Moreover, there are m queries, each query has one of the two types:

Format of the query "1 l r". In reply to the query, you need to add F_{i - l + 1} to each element a_i, where l ≤ i ≤ r.
Format of the query "2 l r". In reply to the query you should output the value of $\text{[math]}$ modulo 1000000009 (10⁹ + 9).

Help DZY reply to all the queries.

Input:

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 300000). The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹) — initial array a.

Then, m lines follow. A single line describes a single query in the format given in the statement. It is guaranteed that for each query inequality 1 ≤ l ≤ r ≤ n holds.

Output:

For each query of the second type, print the value of the sum on a single line.

Sample Input:

Sample Output:

17
12

Note:

After the first query, a = [2, 3, 5, 7].

For the second query, sum = 2 + 3 + 5 + 7 = 17.

After the third query, a = [2, 4, 6, 9].

For the fourth query, sum = 2 + 4 + 6 = 12.

Informação

Provedor Codeforces

Código CF446C