CodeChef: June Challenge | Optimal Xor Set OPTSET | Python, Java, C++ Solution

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Find KK distinct numbers in the range [1,N][1,N] such that the bitwise XOR of all the numbers is maximized. Print any set of these numbers that maximize the XOR.

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Input

  • The first line contains an integer TT, the number of test cases. Then the test cases follow.
  • Each test case contains a single line of input, two integers NN, KK.

Output

For each test case, output KK distinct integers in any order as described in the problem.

Constraints

  • 1≤T≤1041≤T≤104
  • 1≤K≤N≤1061≤K≤N≤106
  • The sum of NN over all queries is at most 4⋅1064⋅106.
  • The sum of KK over all queries is at most 2⋅1062⋅106.

Subtasks

Subtask #1 (5 points):

  • 1≤T≤501≤T≤50
  • 1≤K≤N≤201≤K≤N≤20

Subtask #2 (20 points):

  • 1≤T≤501≤T≤50
  • 1≤K≤N≤2001≤K≤N≤200
  • The sum of NN over all queries is at most 800800.
  • The sum of KK over all queries is at most 400400.

Subtask #3 (75 points): original constraints

Sample Input

3
10 1
9 2
8 7

Sample Output

10
7 8
1 2 3 4 5 6 8

Explanation

Test Case 1: The only possible set is {10}{10} which gives the value 1010.

Test Case 2: The other possible set is {9,6}{9,6} which gives the value 9⊕6=15=7⊕89⊕6=15=7⊕8.

Test Case 3: The only possible set is {1,2,3,4,5,6,8}{1,2,3,4,5,6,8} which gives the value 1⊕2⊕3⊕4⊕5⊕6⊕8=151⊕2⊕3⊕4⊕5⊕6⊕8=15.

Solution

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