Description

You are given two positive integers $N, M$.

Now you need to combine numbers from the sets $A=\{0,1,2,\cdots,N-1\}$ and $B=\{M,\cdots,M+N-1\}$, and select $N$ ordered pairs $(x_i,y_i)$. The requirements are:

• $x_i \in A$, $y_i \in B$, and $x_i \& y_i = x_i$ ($\&$ denotes the bitwise AND operation).
• All $x_i$ are pairwise distinct, and all $y_i$ are pairwise distinct.

Input Format

Input two integers $N, M$.

Output Format

Output a total of $N$ lines.

On the $i$-th line, output two integers $x_i, y_i$, where $x_i \in A, y_i \in B$.

It can be proven that a solution satisfying the conditions always exists.

1 3

0 3

3 5

0 7
1 5
2 6

5 10

0 12
1 13
2 10
3 11
4 14

Hint

Constraints and Notes

For $100\%$ of the testdata, $1 \le N \le M, N+M \le 10^6$.

Explanation

This problem uses a self-written Special Judge. You are welcome to hack it (you can send a private message or post directly).

The scoring of this problem follows the original COCI problem settings, with a full score of $110$.

This problem is translated from COCI2019-2020 CONTEST #3 T5 Sob .

Translated by ChatGPT 5