Default Approximate Comparison

Version: Phuoc Hung OJ Extended

Problem Statement

Two real numbers $a$ and $b$ may differ slightly because of floating-point representation. Determine whether they are approximately equal under Python 3 math.isclose(a, b) with the defaults rel_tol=1e-9 and abs_tol=0.0. The test is $|a-b|\le10^{-9}\max(|a|,|b|)$.

Input

The only line contains real numbers $a$ and $b$, in that order.

Output

Print exactly True if the numbers are close under the default rule; otherwise print exactly False (case-sensitive).

Subtasks

• Subtask 1 (100 points): $a,b$ are finite.

Examples

Example 1

Input

0.30000000000000004 0.3

Output

True

Explanation. The computed difference is approximately 5.55111512313e-17 and the permitted tolerance is 3e-10. The difference is ≤ the tolerance, so the answer is True.

Example 2

Input

1 1.0000000001

Output

True

Explanation. The computed difference is approximately 1.00000008274e-10 and the permitted tolerance is 1.0000000001e-09. The difference is ≤ the tolerance, so the answer is True.

Example 3

Input

1000 1000.01

Output

False

Explanation. The computed difference is approximately 0.00999999999999 and the permitted tolerance is 1.00001e-06. The difference is > the tolerance, so the answer is False.