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EIINTEREST2 - Tet holiday discount

After withdraw money from the bank, Phuc want to find out how much the actual interest rate was applied to his saving account. Please help him. 

Input

The first line contains two integer N and M. These numbers, in turn, denote the amount of money Phuc received and number of months he deposited money into his account. (N < 1018, M ≤ 120)

The second line contains M non-negative integers which are amount of money Phuc put into the account in the  increasing order of time.

Output

A real number which is the actual interest rate (rounded to 3 decimal places) 

Example

Input

Output

50071920 10

3200000 4500000 4200000 6000000 4100000 3500000  4000000 4450000 3750000 3950000

0.033


Added by:Ha Minh Ngoc
Date:2018-12-04
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:CSHARP C++ 4.3.2 CPP CPP14 CPP14-CLANG FSHARP GO JAVA JS-MONKEY NODEJS PHP PYTHON PYPY PYPY3 PYTHON3 RUBY SQLITE SWIFT VB.NET
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