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E3. Summer Homework

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBy the age of three Smart Beaver mastered all arithmetic operations and got this summer homework from the amazed teacher:

You are given a sequence of integers *a* _{1}, *a* _{2}, ..., *a* _{ n}. Your task is to perform on it *m* consecutive operations of the following type:

- For given numbers
*x*_{ i}and*v*_{ i}assign value*v*_{ i}to element*a*_{ x i}. - For given numbers
*l*_{ i}and*r*_{ i}you've got to calculate sum , where*f*_{0}=*f*_{1}= 1 and at*i*≥ 2:*f*_{ i}=*f*_{ i - 1}+*f*_{ i - 2}. - For a group of three numbers
*l*_{ i}*r*_{ i}*d*_{ i}you should increase value*a*_{ x}by*d*_{ i}for all*x*(*l*_{ i}≤*x*≤*r*_{ i}).

Smart Beaver planned a tour around great Canadian lakes, so he asked you to help him solve the given problem.

Input

The first line contains two integers *n* and *m* (1 ≤ *n*, *m* ≤ 2·10^{5}) — the number of integers in the sequence and the number of operations, correspondingly. The second line contains *n* integers *a* _{1}, *a* _{2}, ..., *a* _{ n} (0 ≤ *a* _{ i} ≤ 10^{5}). Then follow *m* lines, each describes an operation. Each line starts with an integer *t* _{ i} (1 ≤ *t* _{ i} ≤ 3) — the operation type:

- if
*t*_{ i}= 1, then next follow two integers*x*_{ i}*v*_{ i}(1 ≤*x*_{ i}≤*n*, 0 ≤*v*_{ i}≤ 10^{5}); - if
*t*_{ i}= 2, then next follow two integers*l*_{ i}*r*_{ i}(1 ≤*l*_{ i}≤*r*_{ i}≤*n*); - if
*t*_{ i}= 3, then next follow three integers*l*_{ i}*r*_{ i}*d*_{ i}(1 ≤*l*_{ i}≤*r*_{ i}≤*n*, 0 ≤*d*_{ i}≤ 10^{5}).

The input limits for scoring 30 points are (subproblem E1):

- It is guaranteed that
*n*does not exceed 100,*m*does not exceed 10000 and there will be no queries of the 3-rd type.

The input limits for scoring 70 points are (subproblems E1+E2):

- It is guaranteed that there will be queries of the 1-st and 2-nd type only.

The input limits for scoring 100 points are (subproblems E1+E2+E3):

- No extra limitations.

Output

For each query print the calculated sum modulo 1000000000 (10^{9}).

Examples

Input

5 5

1 3 1 2 4

2 1 4

2 1 5

2 2 4

1 3 10

2 1 5

Output

12

32

8

50

Input

5 4

1 3 1 2 4

3 1 4 1

2 2 4

1 2 10

2 1 5

Output

12

45

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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