PRATA  Roti Prata
IEEE is having its AGM next week and the president wants to serve cheese prata after the meeting. The subcommittee members are asked to go to food connection and get P (P<=1000) pratas packed for the function. The stall has L cooks (L<=50) and each cook has a rank R (1<=R<=8). A cook with a rank R can cook 1 prata in the first R minutes 1 more prata in the next 2R minutes, 1 more prata in 3R minutes and so on (he can only cook a complete prata) (For example if a cook is ranked 2, he will cook one prata in 2 minutes one more prata in the next 4 mins an one more in the next 6 minutes hence in total 12 minutes he cooks 3 pratas in 13 minutes also he can cook only 3 pratas as he does not have enough time for the 4th prata). The webmaster wants to know the minimum time to get the order done. Please write a program to help him out.
Input
The first line tells the number of test cases. Each test case consist of 2 lines. In the first line of the test case we have P the number of prata ordered. In the next line the first integer denotes the number of cooks L and L integers follow in the same line each denoting the rank of a cook.
Output
Print an integer which tells the number of minutes needed to get the order done.
Example
Input:
3
10
4 1 2 3 4
8
1 1
8
8 1 1 1 1 1 1 1 1
Output:
12
36
1
hide comments
starky:
20210115 09:14:50
use binary search on time space 

shubho5das:
20210115 08:34:02
Solved using Binary Search.


wille_25:
20210114 07:38:15
AC in one go :P 

so7085:
20201228 23:02:51
AC in first go 

ashish707:
20201214 04:09:01
anyone has solution with time complexity < O(P*L) 

anand_undavia:
20201025 17:24:36
"A cook with a rank R can cook 1 prata in the first R minutes 1 more prata in the next 2R minutes"


anand_undavia:
20201025 14:13:16
In the example test case,


akhil_29071991:
20201017 08:28:17
ac in one go 

bismeet:
20200929 15:56:37
Your code has to be in c++ with fastio, else it wont pass anything.


bismeet:
20200929 15:35:40
TLE with Python using BS. 
Added by:  Saransh Bansal 
Date:  20110514 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own problem NTU IEEE codejam 2011 