You are given two integers n and m. Construct such pairs (x, y) from sets A = {0, 1, 2, ..., n − 1} and B = {m, ..., m + n − 1} so that all pairs (x, y) (x ∈ A and y ∈ B) satisfies the condition x & y = x (Here & stands for the bitwise AND operation)

Input

Two integers n and m (1 ≤ n ≤ m, n + m ≤ 106).

Output

Print n lines. In the line i print two integers xi and yi. xi must be in A and yi in B. Each of these pairs that you output must be a matching pair, as specified in the problem statement.

• 0 ≤ xi ≤ n − 1 and for any i ≠ j should be xi ≠ xj
• m ≤ yi ≤ m + n − 1 and for any i ≠ j should be yi ≠ yj

Note

It can be proved that a solution always exists.