# Permutation GCD CodeChef Solution

### We Are Discuss About CODECHEF SOLUTION

Permutation GCD CodeChef Solution

## Problem

Chef is interested in the sum of GCDs of all prefixes of a permutation of the integers \{1, 2, \ldots, N\}.

Next Week Assignment Answers

Formally, for a permutation P = [P_1, P_2, \ldots, P_N] of \{1, 2, \ldots, N\}, let us define a function F_i = \gcd(A_1, A_2, A_3, \ldots, A_i). Chef is interested in the value of F_1 + F_2 + \ldots + F_N.

Now, Chef wants to find a permutation of \{1, 2, \ldots, N\} which has the given sum equal to X. Please help Chef find one such permutation. In case there is no such permutation, print -1. In case of multiple answers, any of them will be accepted.

A permutation of \{1, 2, \ldots, N\} is a sequence of numbers from 1 to N in which each number occurs exactly once.

### Input Format

• The first line of input will contain a single integer T, denoting the number of test cases.
• Each test case consists of a single line containing two space separated integers N and X denoting the length of required permutation and the required sum of GCDs of all prefixes respectively.
Answers will be Uploaded Shortly and it will be Notified on Telegram, So JOIN NOW ### Output Format

• If there is a valid permutation that satisfies the required condition, then:
• In a single line, output N space-separated integers denoting the required permutation permutation.
• If there is no permutation, print -1 in a single line.

### Constraints

• 1 \leq T \leq 10^4
• 1 \leq N \leq 1000
• 1 \leq X \leq 2\cdot N – 1
• The sum of N over all test cases won’t exceed 3\cdot 10^5.

### Sample 1:

Input

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4
1 1
2 1
4 6
3 5

1
-1
2 4 3 1
3 2 1


### Explanation:

Test case 1: The only possible permutation has a sum of 1, as required.

Test case 2: The two permutations of length 2 are:

• [1, 2] with a value of 1 + 1 = 2
• [2, 1] with a value of 2 + 1 = 3

None of them have a sum of X = 1, so we output -1.

Test case 3: For P = [2, 4, 3, 1], we have:

• F_1 = 2
• F_2 = \gcd(2, 4) = 2
• F_3 = \gcd(2, 4, 3) = 1
• F_4 = \gcd(2, 4, 3, 1) = 1

The sum of these values is 6, as required.

## SOLUTION

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