CodeForces768B：Code For 1 （分治）

Posted 2020-11-09 ---学习ing---

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 1s 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?

Input

The first line contains three integers n, l, r (0 ≤ n < 2⁵⁰, 0 ≤ r - l ≤ 10⁵, 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

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

Examples

Input

7 2 5

Output

4

Input

10 3 10

Output

5

Note

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.

 

题意：一开始有一个数N，每次把所有大于1的数变为x/2，x%2，x/2。知道不能操作。样例如题。

思路：找规律我们得知，最后的01串有很多的对称性。首先推出最后一层有num=2^(lg2(N)+1) -1个数，并且以x=(num+1)/2为对称轴，所以如果在对称轴的右边，我们可以把它对称到x轴的左边。   然后把对称轴左边的区间[1,x]又看成一个整体，它又以x2=(x+1)/2为对称轴，如果在x2右边，又把它对称到x2左边.....一直对称下去，直到把它对称到一个对称轴上。而我们可以求出对称轴上对应的数的值，就是N的二进制对应的数。

          比如10的二进制表示为10（ten）=1010(two)。10=1（1）+0（2）+1（4）+0（8），（括号里的是最后一层的对称轴位置，也是最后一层二进制对应位置的结果）。

（ps：也可以用分形来做。

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=100010;
ll find(ll x){
    ll y=log2(x);
    if(1LL<<y==x) return y;
    return find((1LL<<(y+1))-x);
}
int main()
{
    ll N,L,R,ans=0,Bit;
    cin>>N>>L>>R;
    Bit=log2(N);
    for(ll i=L;i<=R;i++)
        ans+=(N>>(Bit-find(i)))&1LL;
    cout<<ans<<endl;
    return 0;
}