A10828. Code For 1

Jon fought bravely to rescue the wildlings who were attacked by the white-walkers at Hardhome. On his arrival, Sam tells him that he wants to go to Oldtown to train at the Citadel to become a maester, so he can return and take the deceased Aemon's place as maester of Castle Black. Jon agrees to Sam's proposal and Sam sets off his journey to the Citadel. However becoming a trainee at the Citadel is not a cakewalk and hence the maesters at the Citadel gave Sam a problem to test his eligibility.

Initially Sam has a list with a single element $n$ . Then he has to perform certain operations on this list. In each operation Sam must remove any element $x$ , such that $x>1$ , from the list and insert at the same position , ,  sequentially. He must continue with these operations until all the elements in the list are either $0$ or $1$ .

Now the masters want the total number of $1$ s in the range $l$ to $r$ ( $1$ -indexed). Sam wants to become a maester but unfortunately he cannot solve this problem. Can you help Sam to pass the eligibility test?

The first line contains three integers $n$ , $l$ , $r$ ( $0<=n<2^{50}$ , $0<=r-l<=10^{5}$ , $r>=1$ , $l>=1$ ) – initial element and the range $l$ to $r$ .

It is guaranteed that $r$ is not greater than the length of the final list.

Output the total number of $1$ s in the range $l$ to $r$ in the final sequence.

Consider first example:


Elements on positions from $2$ -nd to $5$ -th in list is $[1,1,1,1]$ . The number of ones is $4$ .

For the second example:


Elements on positions from $3$ -rd to $10$ -th in list is $[1,1,1,0,1,0,1,0]$ . The number of ones is $5$ .