All Tracks Data Structures Advanced Data Structures Segment Trees Problem

Zeus and Fibonacci
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Data Structures, Data Structures, Matrix Exponentiation, Segment tree

Problem
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You are given an array A consisting of N integers. You have to process two types of queries on this array.
Type 1: Change the ith element to X
Type 2: Given l and r, calculate: \(\sum_{i=l}^{r} \sum_{j=i}^{r} Fib ( \sum_{k=i}^{j} A_k ) \)

Note: \(Fib(i)\) is the ith Fibonacci number. \(Fib(0)=0 \space.\space Fib(1)=1 \)

Input

First line contains an integer N.
Next line contains N space separated integers denoting array A.
Next line contains the integer Q.
Next Q lines are of the following format:
\(1 \space i \space X\) : for type 1 query
\(2 \space l \space r\) : for type 2 query

Output

For each type 2 query output the answer modulo \(10^9+7\) on a new line.

Constraints

\(1 ≤ N,Q ≤ 10^5\)
\(1 ≤ A[i],x ≤ 10^9\)
\(1 ≤ l,r,i ≤ N \)
\(l ≤ r \)

SAMPLE INPUT
3
1 2 3
2
2 1 2
2 1 3
SAMPLE OUTPUT
4
19
Explanation

Query 1:
possible subarrays : (1),(2),(1,2)
Corresponding sums : 1 ,2 ,3
Corresponding fibonacci: 1 , 1, 2
Sum of fibnoacci : 1 + 1+2=4
output : 4%(10^9+7)=4
Query 2:
possible subarrays : (1),(2),(3),(1,2),(2,3),(1,2,3)
Corresponding sums : 1,2,3,3,5,6
Corresponding fibonacci: 1,1,2,2,5,8
Sum of fibnoacci : 19
output : 19%(10^9+7)=19

Time Limit: 2,0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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