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Sum Of Infinite Array

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Contributed by
Ashwani
Medium
yellow-spark
0/80
35 mins
70 %
3317 upvotes
Zensar TechnologiesHexaware TechnologiesTata Consultancy Services (TCS)
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Problem Statement

Given an array “A” of N integers and you have also defined the new array “B” as a concatenation of array “A” for an infinite number of times.

For example, if the given array “A” is [1,2,3] then, infinite array “B” is [1,2,3,1,2,3,1,2,3,.......].

Now you are given Q queries, each query consists of two integers “L“ and “R”(1-based indexing). Your task is to find the sum of the subarray from index “L” to “R” (both inclusive) in the infinite array “B” for each query.

Note :

The value of the sum can be very large, return the answer as modulus 10^9+7.
Detailed explanation ( Input/output format, Notes, Images )
Constraints :
1 <= T <= 100
1 <= N <= 10^4   
1 <= A[i] <= 10^9
1 <= Q <= 10^4
1 <= L <= R <= 10^18

Time Limit: 1sec
Sample Input 1 :
1
3
1 2 3
2
1 3
1 5
Sample Output 1 :
6 9
Explanation to Sample Input 1 :
For the first test case, the given array A is [1,2,3] therefore the infinite array “B” will be [1,2,3,1,2,3,1,2,3,.......]. So the answer for the given first query is 6 because the sum of the subarray from index 1 to 3 of infinite array “B” i.e. (B[1]+B[2]+B[3]) is 6.

For the given second query is 9 because the sum of the subarray from index 1 to 5 of array “B” .ie (B[1]+B[2]+B[3]+B[4]+B[5]) is 9.
Sample Input 2 :
1
4
5 2 6 9
3
1 5
10 13
7 11
Sample Output 2 :
27 22 28
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