Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n2) and runtime should be under 1 second. Apply dynamic programming. Do not use recursion. Make sure ALL test cases return expected outputs.Output FormatFor each query, output one line containing an integer Dn. The number must be output mod (109 + 7).Sample Input 0:501234Sample Output 0:10129Edge Case: (to test against runtime and timeout error)300000 (number of queries)300000300000300000300000...and so on until there are 300,000 of them The actual code:def solve(n): MOD = 1000000007 # compute and return answer here q = int(input().rstrip())outs = []for i in range(q): n = int(input().rstrip()) outs.append(solve(n))print("{}".format("\n".join(list(map(str,outs))))) A derangement of N objects is a permutation wherein none of the N objects are in the correct position. Forexample, for the set 1, 2, 3, the arrangements are• 1, 2, 3• 1,3,2• 2,1,33, 2, 1Since in the first 2 permutations, 1 is in the correct spot. In the 1st and 4th permutation, 2 is in the right spot.In the 1st and 3rd permutation, 3 is in the correct spot. Therefore the derangements are• 2, 3, 13,1,2The formula for the number of derangements for N objects is defined as:Do = 1D₁ = 0Dn = (Dn−1 + Dn-2) · (n − 1) for n ≥ 2You have to answer Q queries. Each query consists of an integer n. You must compute for D. This numbermay be very large, so output it mod 10⁹ +7.Input FormatInput starts with one line containing a single integer Q, indicating the number of queries.Qlines follow, each containing a single integer n.Constraints1≤Q≤3.1050 ≤ n ≤ 3.105

Dynamic programming is a technique in computer programming that helps to efficiently solve a class…

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Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n²) and runtime should be under 1 second. Apply dynamic programming. Do not use recursion. Make sure ALL test cases return expected outputs.

Output Format
For each query, output one line containing an integer D_n. The number must be output mod (10⁹ + 7).

Sample Input 0:
5
0
1
2
3
4

Sample Output 0:
1
0
1
2
9

Edge Case: (to test against runtime and timeout error)
300000 (number of queries)
300000
300000
300000
300000
...
and so on until there are 300,000 of them

The actual code:

def solve(n):

MOD = 1000000007

# compute and return answer here

q = int(input().rstrip())

outs = []

for i in range(q):

n = int(input().rstrip())

outs.append(solve(n))

print("{}".format("\n".join(list(map(str,outs)))))

A derangement of N objects is a permutation wherein none of the N objects are in the correct position. For
example, for the set 1, 2, 3, the arrangements are
• 1, 2, 3
• 1,3,2
• 2,1,3
3, 2, 1
Since in the first 2 permutations, 1 is in the correct spot. In the 1st and 4th permutation, 2 is in the right spot.
In the 1st and 3rd permutation, 3 is in the correct spot. Therefore the derangements are
• 2, 3, 1
3,1,2
The formula for the number of derangements for N objects is defined as:
Do = 1
D₁ = 0
Dn = (Dn−1 + Dn-2) · (n − 1) for n ≥ 2
You have to answer Q queries. Each query consists of an integer n. You must compute for D. This number
may be very large, so output it mod 10⁹ +7.
Input Format
Input starts with one line containing a single integer Q, indicating the number of queries.
Qlines follow, each containing a single integer n.
Constraints
1≤Q≤3.105
0 ≤ n ≤ 3.105

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