[Solution] The XOR-OR Dilemma CodeChef Solution

Chef has an array A$A$ of length N$N$ such that Ai=i$A_i=i$.

In one operation, Chef can pick any two elements of the array, delete them from A$A$, and append either their bitwise XOR or their bitwise OR to A$A$.

Note that after each operation, the length of the array decreases by 1$1$.

Let F$F$ be the final number obtained after N−1$N-1$ operations are made. You are given an integer X$X$, determine if you can get F=X$F=X$ via some sequence of operations.

In case it is possible to get F=X$F=X$, print the operations too (see the section Output format for more

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 details), otherwise print −1$-1$.

Input Format

• The first line of input will contain a single integer T$T$, denoting the number of test cases.

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The XOR-OR Dilemma CodeChef Solution

• Each test case consists of a single line containing two space-separated integers N$N$ and X$X$.

Output Format

For each test case, output −1$-1$ if it is impossible to get X$X$ in the end. Otherwise print N−1$N-1$ lines denoting the operations.

On each line, print

• 1 x y$1xy$ if you want replace x$x$ and y$y$ with x OR y$xORy$.
• 2 x y$2xy$ if you want replace x$x$ and y$y$ with x XOR y$xXORy$.

Note that x$x$ and y$y$ are the elements of the array at the time of applying the operation, and if either of them is not present in the array you will receive a WA verdict.

Constraints

• 1≤T≤5000$1\le T\le 5000$
• 2≤N≤215$2\le N\le 2^{15}$
• 1≤X≤216−1$1\le X\le 2^{16}-1$
• The sum of N$N$ over all test cases won't exceed 2⋅105