Salazar Slytherin's Locket

题意翻译

求$l...r$之间转成$b$进制后，$0,1,2...,b-2,b-1$都出现偶数次的数的个数。 第一行一个数$q$,为数据组数。 下面$q$行，每行$3$个整数，表示$b,l,r$。 $1\le q \le 10^5$ $2\le b \le 10$ $1\le l \le r \le 10^{18}$ 输出，共$q$行，为每个询问的答案。

题目描述

Harry came to know from Dumbledore that Salazar Slytherin's locket is a horcrux. This locket was present earlier at 12 Grimmauld Place, the home of Sirius Black's mother. It was stolen from there and is now present in the Ministry of Magic in the office of Dolorous Umbridge, Harry's former Defense Against the Dark Arts teacher. Harry, Ron and Hermione are infiltrating the Ministry. Upon reaching Umbridge's office, they observed a code lock with a puzzle asking them to calculate count of magic numbers between two integers $ l $ and $ r $ (both inclusive). Harry remembered from his detention time with Umbridge that she defined a magic number as a number which when converted to a given base $ b $ , all the digits from $ 0 $ to $ b-1 $ appear even number of times in its representation without any leading zeros. You have to answer $ q $ queries to unlock the office. Each query has three integers $ b_{i} $ , $ l_{i} $ and $ r_{i} $ , the base and the range for which you have to find the count of magic numbers.

输入输出格式

输入格式

First line of input contains $ q $ ( $ 1<=q<=10^{5} $ ) — number of queries. Each of the next $ q $ lines contain three space separated integers $ b_{i} $ , $ l_{i} $ , $ r_{i} $ ( $ 2<=b_{i}<=10 $ , $ 1<=l_{i}<=r_{i}<=10^{18} $ ).

输出格式

You have to output $ q $ lines, each containing a single integer, the answer to the corresponding query.

输入输出样例

输入样例 #1

2
2 4 9
3 1 10

输出样例 #1

1
2

输入样例 #2

2
2 1 100
5 1 100

输出样例 #2

21
4

说明

In sample test case $ 1 $ , for first query, when we convert numbers $ 4 $ to $ 9 $ into base $ 2 $ , we get: - $ 4=100_{2} $ , - $ 5=101_{2} $ , - $ 6=110_{2} $ , - $ 7=111_{2} $ , - $ 8=1000_{2} $ , - $ 9=1001_{2} $ . Out of these, only base $ 2 $ representation of $ 9 $ has even number of $ 1 $ and $ 0 $ . Thus, the answer is $ 1 $ .

题意翻译

求$l...r$之间转成$b$进制后，$0,1,2...,b-2,b-1$都出现偶数次的数的个数。 第一行一个数$q$,为数据组数。 下面$q$行，每行$3$个整数，表示$b,l,r$。 $1\le q \le 10^5$ $2\le b \le 10$ $1\le l \le r \le 10^{18}$ 输出，共$q$行，为每个询问的答案。