Problem2983--DZY Loves Fibonacci Numbers

2983: DZY Loves Fibonacci Numbers

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

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

  1. Format of the query "1 l r". In reply to the query, you need to add Fi-l+1 to each element ai, where l≤i≤r.
  2. Format of the query "2 l r". In reply to the query you should output the value of 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,...,an(1≤ai≤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.

Examples
Input
4 4
1 2 3 4
1 1 4
2 1 4
1 2 4
2 1 3
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.

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