PRATA - Roti Prata

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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
shubhamphpefy: 2022-12-16 20:20:01

Last edit: 2022-12-16 20:20:44
jeet_manojit: 2022-09-14 06:05:25

Last edit: 2022-09-14 08:07:04
ayush_7901: 2022-06-28 20:01:11

Done in 1st go. Nice and Conceptual Problem.
Hint 1 : understand the problem correctly
Hint 2 : estimate the largest time required correctly

piyushkrs: 2022-03-15 20:55:00

Hint 1: sum of 1st n natural number is n*(n + 1) / 2
Hint 2(in case of TLE in binary Search): high = maximum time to get p paratas not INT_MAX

tejas07_psk: 2022-02-21 18:30:47

If for python 3 you occasionally get tle use Python 2 (PyPy 2.7.13) , syntax is almost similar.
Although for this question Python 3 works just fine, maybe you are doing something wrong.
As a suggestion I would say for each mid time in outer search space, use AP quadratic formula to calculate the potential number of parathas don't use 2 nested loops even though in constraints it says L <= 50.
For python 2 take care of float division.

Last edit: 2022-02-21 18:34:06
ankit_mzp: 2021-12-24 14:45:17

The reason answer for first use case P = 10, R[] = [1,2,3,4], Ans = 12 is:
1. Let's take answer as 10 so:
* first will make (1+2+3+4 = 10min) i.e. 4Prata
* Second will make (2 + 4 = 6min) i.e. 2Prata. Note we cannot take 3rd prata time as total time will become 2 + 4 + 6 = 12min in that case
* Third will make (3 + 6 = 9min) i.e. 2 Prata
* Fourth will make (4min) i.e. 1Prata
So if time = 10 then Prata = 4 + 2 + 2 + 1 = 9 Prata
And similarly to make 10Prata min time will be 12min

avishjain2002: 2021-10-25 18:15:31

beatrock why are you taking the rank 4 cook two times the starting four means that there are four cooks see input

beatrock: 2021-09-11 17:39:00

why we need 12 min in 1st example?
we can do it in 10
1 will cook 4 in 10 min
2 will cook 2 in 6 min
3 will cook 2 in 9 min
4s will cook 1 each in 4 min
4+2+2+1+1 = 10
Ohh understod first integer indicates the no of cooks so here 4 in not the rank of cook rather it is no of cook

Last edit: 2021-09-11 17:44:40
sj_2330: 2021-09-05 09:52:22

great question

bappa_10: 2021-08-14 13:23:18

what will be the max required time in worst case...???


Last edit: 2021-08-14 13:23:44

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