# Pairwise Xors Codechef Solution | APRIL CHALLENGE Share:

Pairwise Xors Codechef Solution

JJ gives Chef a number XX and challenges Chef to come up with three distinct numbers A,A, B,B, and CC such that:

• 0≤A,B,C<2300≤A,B,C<230;
• (A⊕B)+(B⊕C)+(C⊕A)=X(A⊕B)+(B⊕C)+(C⊕A)=X.

Help Chef come up with three such numbers or determine that no such tuple exists.

Here, ⊕⊕ denotes the bitwise XOR operation.

### Input Format

• The first line contains a single integer TT – the number of test cases. Then the test cases follow.
• The first and only line of each test case contains an integer XX – the number mentioned in the problem statement.

### Output Format

For each test case, output three distinct numbers AA, BB and CC (0≤A,B,C<230)(0≤A,B,C<230) such that (A⊕B)+(B⊕C)+(C⊕A)=X(A⊕B)+(B⊕C)+(C⊕A)=X.

If multiple such tuples exist, print any. If no such tuple exists, print −1−1.

### Constraints

• 1≤T≤10001≤T≤1000
• 1≤X<2301≤X<230

### Sample Input 1

``````3
6
3
20
``````

### Sample Output 1

``````0 1 3
-1
3 11 1
``````

### Explanation

Test Case 11: A=0,B=1,C=3A=0,B=1,C=3 is a valid answer because (0⊕1)+(1⊕3)+(3⊕0)=1+2+3=6(0⊕1)+(1⊕3)+(3⊕0)=1+2+3=6.

Test Case 22: It can be proven that no tuple exists that satisfies the given conditions.

Test Case 33: A=3,B=11,C=1A=3,B=11,C=1 is a valid answer because (3⊕11)+(11⊕1)+(1⊕3)=8+10+2=20(3⊕11)+(11⊕1)+(1⊕3)=8+10+2=20.