MATHLOVE - Math is Love


Rashid loves mathematics. He recently started to learn how the various function works in mathematics. On his journey through the math world, he came in touch with a function named Y.

He also came to know that, here Y means the summation of number from 0 to n. For example if n = 5, then 

Y = 0+1+2+3+4+5 = 15.

Now he is wondering if the knows the value of Y, can he find the value of n for the above equation?

Being so very new to the math world, he could not figure out how to approach this new problem. So he came to you for help. Can you help him?



First line of input will be T(1<=T<=100000), denoting the number of test cases.

Next T lines will contain the number Y(1<=Y<=3*10^9), value of the above function.



For each test case, if there is exist a value of n for which the above function gives the output Y then print

that value of n, otherwise if print “NAI”. (quotes for clarification).


Note: Data set is huge, use scanf,printf for faster input, output. 


Sample Input

Sample Output















hide comments
sanyam19: 2018-06-07 11:57:08

easy 1.... use double for decimal but remember of changing into an integer as a final ans... :)

aadarsh45: 2018-04-06 17:26:51

Use long long int instead of double , i got 3 WA because of this

ayushgupta1997: 2017-09-27 22:10:43

No actual binary search required, tried precomputation didn't worked failed on test case 5,simple number theory brute force works out beautifully :D

avi_pandey: 2017-07-19 14:28:11

easy problem . AC in one go . use inputs in double.

Marcin: 2017-05-28 00:03:08

There is definitely something wrong with the upper bound of the input. I got WA for 3*10^9, but correct for 10*10^9. After first few steps on doing binary search on submissions, I found that the upper bound is somewhere between 4.9*10^9 and 6.4*10^9

Shubham Jadhav: 2017-05-10 20:25:27

easy points :)

candide: 2017-04-10 12:45:55

@shreeshiv : 0 is not a valid input (because1<=Y<=3*10^9) but my own code gives answer=0. BTW, you can try Online SPOJ toolkit.

Last edit: 2017-04-11 21:25:19
shreeshiv: 2017-04-09 22:34:02

what is answer for 0 ,NAI or 0

xralier: 2017-04-07 08:42:41

anyone got AC in JAVA ? im getting TLE .. im solving this by bottom to top DP then applying binary search. I dont get it , why a problem forcing a programmer to use c/c++ ?

candide: 2017-04-06 18:08:18

Too easy for a classical problem. Not really brute force nor binary search, better : use basic math. Good for testing your input/output skills ;)

Last edit: 2017-04-09 14:45:37

Added by:Jamil Siam
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)