Exact a to the power b

Time limit1sMemory limit256 MB

Summary

Print the exact value of a to the power b for a decimal base without rounding or dropping digits.

Level: Medium4 of 10
Topics: Implementation, Math, String
Solved: No attempts yet

Problem

You are given a real number $a$ and an integer $b$ . Write a program that computes $a^b$ exactly, with no rounding error.

The fractional part of $a$ has finitely many digits, so $a^b$ is also a finite decimal. Double precision floating point does not hold enough digits for it, so compute with integer arithmetic.

Input

The first line contains $a$ and $b$ , separated by a space. ( $0 < a < 100$ , $1 \le b \le 100$ )

$a$ always contains a decimal point and has at most 9 digits after it. The last digit after the decimal point is not 0.

Output

Print the exact value of $a^b$ on the first line.

If $a$ has $k$ digits after the decimal point, the answer has exactly $k \times b$ digits after the decimal point. Do not round, do not drop digits, and do not append extra zeros. When the integer part is 0, the line starts with 0..

Examples3

Example 1
Input
```
3.141592 3
```
Expected output
```
31.006257328285746688
```
Example 2
Input
```
0.1 10
```
Expected output
```
0.0000000001
```
Example 3
Input
```
1.01 5
```
Expected output
```
1.0510100501
```