Perfect match

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 ≤ 10^6).

Output

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

• 0 ≤ x[i] ≤ n − 1 and for any i ≠ j should be x[i] ≠ x[j]

• m ≤ y[i] ≤ m + n − 1 and for any i ≠ j should be y[i] ≠ y[j]

Examples

Note

It can be proved that a solution always exists.