Sherlock and the Encrypted Data

2000ms

524288K

Description:

Sherlock found a piece of encrypted data which he thinks will be useful to catch Moriarty. The encrypted data consists of two integer l and r. He noticed that these integers were in hexadecimal form.

He takes each of the integers from l to r, and performs the following operations:

He lists the distinct digits present in the given number. For example: for 1014₁₆, he lists the digits as 1, 0, 4.
Then he sums respective powers of two for each digit listed in the step above. Like in the above example sum = 2¹ + 2⁰ + 2⁴ = 19₁₀.
He changes the initial number by applying bitwise xor of the initial number and the sum. Example: $\text{[math]}$ . Note that xor is done in binary notation.

One more example: for integer 1e the sum is sum = 2¹ + 2¹⁴. Letters a, b, c, d, e, f denote hexadecimal digits 10, 11, 12, 13, 14, 15, respertively.

Sherlock wants to count the numbers in the range from l to r (both inclusive) which decrease on application of the above four steps. He wants you to answer his q queries for different l and r.

Input:

First line contains the integer q (1 ≤ q ≤ 10000).

Each of the next q lines contain two hexadecimal integers l and r (0 ≤ l ≤ r < 16¹⁵).

The hexadecimal integers are written using digits from 0 to 9 and/or lowercase English letters a, b, c, d, e, f.

The hexadecimal integers do not contain extra leading zeros.

Output:

Output q lines, i-th line contains answer to the i-th query (in decimal notation).

Sample Input:

1
1014 1014

Sample Output:

Sample Input:

2
1 1e
1 f

Sample Output:

1
0

Sample Input:

2
1 abc
d0e fe23

Sample Output:

412
28464

Note:

For the second input,

14₁₆ = 20₁₀

sum = 2¹ + 2⁴ = 18

$\text{[math]}$

Thus, it reduces. And, we can verify that it is the only number in range 1 to 1e that reduces.

Informação

Provedor Codeforces

Código CF776G