Percentage Error

Version: Phuoc Hung OJ Extended

Problem Statement

Given an approximate value $x$ and a nonzero reference value $ref$, calculate the relative error $r=\dfrac{|x-ref|}{|ref|}$. Display it as a percentage, namely $100r$ with exactly 3 digits after the decimal point and a trailing % symbol.

Input

The only line contains the approximate real value $x$ and reference value $ref$.

Output

Print the percentage error with exactly 3 decimal places and a trailing %.

Subtasks

• Subtask 1 (100 points): $x,ref$ are finite; $ref\ne0$.

Examples

Example 1

Input

99.9 100

Output

0.100%

Explanation. Substituting the input into the formula gives |99.9-(100)|/|100| ≈ 0.001. Converting to a percentage with three decimal places produces 0.100%.

Example 2

Input

1.01 1.0

Output

1.000%

Explanation. Substituting the input into the formula gives |1.01-(1.0)|/|1.0| ≈ 0.01. Converting to a percentage with three decimal places produces 1.000%.

Example 3

Input

-9.9 -10.0

Output

1.000%

Explanation. Substituting the input into the formula gives |-9.9-(-10.0)|/|-10.0| ≈ 0.01. Converting to a percentage with three decimal places produces 1.000%.