please find the error, why it is not working for subtask2

Here is the link code

Well, your code shows different output when compared with my code:

Input: N= 2[fixed] & varying from K = 10^10 to k = 10 ^18

Your Output: for N = 2, K = 10^10 is 544142479

Mine: 2485

Similarly, with

Inputs Like : N = 2, K = 10^11

Your output: 185020288

Mine: 245350, Maybe I got Lucky here

PLEASE Correct me if I’m wrong. Here is my AC code https://www.codechef.com/viewsolution/24647123

Hey!

Can you please explain your code. A little explanation on how do you come up with this algorithm will work.

Idea: Consider N = 2 and K = 100, so we have to use the values that are in the range [100, 101] and find out the total number of values that are unreachable. The values that are lower than K are definitely unreachable, here the values {1,2,3,4,5,6,…99} are unreachable. (i. e nothing but (K - 1) number of values = (100 - 1) = 99). Now, moving onto values that are greater than K and lower than second multiple of K( K * 2 = 100 * 2 = 200) , here in this case {102, 103, 104, 105,106,…199} are unreachable. (these are 98 in total). Now, moving onto values that are lower than 3rd multiple of K which is nothing but (K * 3 = 100 * 3 = 300) , we have {203, 204, 205, … 299) values are unreachable(97 in total). It following a pattern of AP Series with last term as 99 having a common difference between the numbers as 1.

Pattern = 99 + 98 + 97 + …1

Well, the first term may differ according with the case that involves, here the first term a = 1;

No. Of terms here = n = 99

So, the sum formula = n/2(2a + (n - 1)*d) = 4950 (in this case) ;
Generalizing all the cases:
Pattern : a, a + d, a + 2*d, a + 3*d, … a + (n-1)*d.

Last Term = K - 1;

Difference d = (N + K - 1) - K = N - 1;

No of terms (n) = Last term / Difference = L / d;

First Term a = Last Term - (No.of terms - 1) * Common difference = L - (n - 1)*d;

Sum(No. of Unreachable Values) = (No .of Terms * a) + (1 + 2 + 3 + 4+…(no. of terms - 1)) * Common difference;

we know that : 1 + 2 + 3 +… n - 1 terms sum is nothing but (n * (n-1)) / 2;

Lets suppose this sum be j, therefore j = (n * (n-1))/2;

Therefore, Sum(No. of unreachable Values) = (n * a) + (j * d);

That’s it We are Done !

Hope it helps.

NOTE : N is Given input , n is no .of terms

Thank you!

In your code in line number 28 the formula is not correct. (a/b)%m is not equal to ((a%m)/(b/%m))%m. But instead it should be ((a%m)*((b^-1)%m)%m)%m , where b^-1 is the multiiplicative modulo inverse of b with m. I guess you got lucky here.

Yeah, I’ve actually forgotten to remove the %m after ‘/2’. But It works in both the cases(removal of %m and non removal of %m after ‘/2’). Thanks for Pointing out !