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

Added by:Saransh Bansal
Date:2011-05-14
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Own problem- NTU IEEE codejam 2011

hide comments
2020-04-04 23:04:54
AC in one Go!! ;)
2020-01-27 12:34:13
binary search + quadratic equation rocks
2019-12-24 15:41:37
Binary Search and AC in one go!
2019-09-13 18:09:59
AC with Binary Search
2019-08-03 22:56:35
let max_rank=(the max rank in the given array)
let p=number of prata req.
upper_limit=(p*(2*max_rank+(p-1)*max_rank))/2 (sum of p terms in ap)
2018-11-11 18:26:25
Had to learn Min Heap and Priority Queue just to solve this. And finally ac :)

Last edit: 2018-11-11 18:26:43
2018-11-01 11:55:55
Set upper limit as 10000007 in Java, it gives TLE with 10^9 :)
2018-10-04 19:22:49
Binary Search AC in one go!!
2018-10-02 20:16:28
I agree with @pallindromeguy
you should take upper limit quite high
2018-09-03 21:10:11
#40 :)
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