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Beautiful Array CodeChef Solution

Beautiful Array CodeChef Solution

Problem

You’re given an array¬†A¬†of¬†N¬†integers. You need to find the minimum cost of creating another array¬†B¬†of¬†N¬†integers with the following properties

  • B_i \ge 0¬†for each¬†1 \leq i \leq N
  • The GCD of adjacent elements of¬†B¬†is equal to¬†1, i.e,¬†\gcd(B_i, B_{i+1}) = 1¬†for each¬†1 \leq i \lt N

Next Week Assignment Answers

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The cost of creating B is defined as follows:

\sum_{i=1}^{N} 2^{|A_i – B_i |}

Find the minimum possible cost to create the array B. Since the answer can be huge print it modulo 10^9+7

Note: You need to minimize the value of total cost of creating the array B, and then print this minimum value modulo 10^9 + 7. For example, suppose there is a way to create the required B with a cost of 500, and another way to do it with a cost of 10^9 + 7 (which is 0 \pmod {10^9 + 7}). The output in this case would be 500 and not 0.

Input Format

  • The first line of input will contain a single integer¬†T, denoting the number of test cases.
  • The first line of each test case contains an integer¬†N¬†– the length of the array¬†A
  • The second line of each test case contains¬†N¬†space-separated integers¬†A_1,A_2,\ldots,A_N
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Output Format

For each test case, output on a new line the minimum cost of creating the array B, modulo 10^9 + 7.

Constraints

  • 1 \leq T \leq 150
  • 1 \leq N \leq 10^4
  • 1 \leq A_i \leq 10^6
  • The sum of¬†N¬†over all test cases won’t exceed¬†10^4.

Sample 1:

Input

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Output

3
3
15 16 19
2
5 10
7
9 15 7 19 10 7 1

 

3
3
8

 

Explanation:

Test case 1: The given input already satisfies all the conditions, hence we can take B = A with a cost of 2^0 + 2^0 + 2^0 = 3.

Test case 2: One optimal way is to choose B as [ 5, 11 ], with a cost of 2^0 + 2^1 = 3.

SOLUTION

Beautiful Array CodeChef Solution

SOLUTION

Beautiful Array CodeChef Solution

SOLUTION

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