Near-Zero Comparison

Version: Phuoc Hung OJ Extended

Problem Statement

Given a real number $x$ and a nonnegative absolute tolerance $eps$, decide whether $x$ is close to zero by testing $|x|\le eps$. This is the result of Python 3 math.isclose(x, 0.0, rel_tol=0.0, abs_tol=eps).

Input

The only line contains real number $x$ and absolute tolerance $eps$, in that order.

Output

Print exactly True if $|x|\le eps$, otherwise False.

Subtasks

• Subtask 1 (100 points): $x,eps$ are finite and $eps\ge0$.

Examples

Example 1

Input

1e-10 1e-09

Output

True

Explanation. The computed difference is approximately 1e-10 and the permitted tolerance is 1e-09. The difference is ≤ the tolerance, so the answer is True.

Example 2

Input

1e-06 1e-09

Output

False

Explanation. The computed difference is approximately 1e-06 and the permitted tolerance is 1e-09. The difference is > the tolerance, so the answer is False.

Example 3

Input

0 1e-12

Output

True

Explanation. The computed difference is approximately 0 and the permitted tolerance is 1e-12. The difference is ≤ the tolerance, so the answer is True.