Problem Description

You are given integers $n$ and $k$. Your goal is to pick $n$ distinct integer points on the $xy$-plane such that for exactly $k$ pairs of points, the Euclidean distance between the points is an integer. Recall that the Euclidean distance between points $(x_1, y_1)$ and $(x_2, y_2)$ is

It can be shown that a solution always exists under the constraints of this task.

Input Format

The only line contains two integers, $n$ and $k$.

Output Format

Print $n$ lines with the $i$th line containing two integers: the $x$ and $y$ coordinates of the $i$th point. The absolute value of every coordinate must be at most $10^9$.

If there are multiple solutions, you can print any of them.

3 2

1 1
1 2
2 2

Hint

Explanation

The Euclidean distance between $(1, 1)$ and $(1, 2)$ is $1$. The distance between $(1, 2)$ and $(2, 2)$ is also $1$. However, the distance between $(1, 1)$ and $(2, 2)$ is $\sqrt 2$, which is not an integer.

Constraints

• $1 \le n \le 100$
• $0 \le k \le n(n - 1) / 2$

Scoring