AE2A  Dice
Jack claims that he has telekinetic powers. He has made a bet with Mike that he would throw a die n times and would get exactly k pips in total. Jack's die has 6 faces with numbers from 1 to 6 written on them and is perfectly symmetric. Mike does not believe in Jack's telekinetic powers (in general, being a tenacious rationalist, he does not believe in telekinesis), but he is concerned that Jack could win the bet simply by luck. Therefore, he would like to know what is the chance (in percent) of such an unlucky event, and asked you to write a program that would help him solve this problem.
Input
The first line of the standard input contains a single integer t (1 ≤ t ≤ 20) denoting the number of test cases. Each of the following t lines contains a description of one test case in the form of two integers n_{i} and k_{i} (1 ≤ n_{i}, k_{i} ≤ 10^{6}) separated by a single space.
Output
To the standard output t lines should be written, containing the answers to respective test cases. The answer to one test case is the probability (in percent) that Jack wins the bet, rounded down to the nearest integer.
Example
For the input data:
1 1 6
the correct result is:
16
Task author: Jakub Onufry Wojtaszczyk.
hide comments
rohitjain00:
20190417 18:33:54
Repeat Comment But needs to be on top :


ab_biswas09:
20190318 15:52:24
Great Problem >> 

hkyiitd:
20190308 11:45:17
Worst platform , with worst explanation of problems. 

skshivam64:
20180904 09:59:12
For i throws, the probability of getting (i + 6i) / 2 pips is maximum. Find the value of i for which this maximum is zero because for i+1 throws the probability of getting any number of pips is smaller than the maximum probability for the case of i throws. I found the desired i to be 546. 

alysalhab5:
20180227 13:50:02
explain more plz


bharatgoyal:
20180106 08:11:07
@Shubham Matta, how did you get these bounds? Some mathematical formula? 

kmkhan_014:
20171210 15:09:07
poorly explained!! 

Shubham Jadhav:
20170519 15:23:31
Nice Problem :) 

big_o_logn:
20170514 22:04:52
AC first try, use the bounds mentioned in the comments and a memo table of doubles 

ssunitk:
20170509 21:41:11
Last edit: 20170509 21:44:43 
Added by:  Race with time 
Date:  20090503 
Time limit:  0.150s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Algorithmic Engagements 2009 