CF BUDDY

Problem: During their training for the ICPC competitions, team "Jee You See" stumbled upon a very basic counting problem. After many "Wrong answer" verdicts, they finally decided to give up and destroy turn-off the PC. Now they want your help in up-solving the problem.

You are given 4 integers $n$ , $l$ , $r$ , and $z$ . Count the number of arrays $a$ of length $n$ containing non-negative integers such that:

$l\le a_1+a_2+\ldots+a_n\le r$ , and
$a_1\oplus a_2 \oplus \ldots\oplus a_n=z$ , where $\oplus$ denotes the bitwise XOR operation.

Since the answer can be large, print it modulo $10^9+7$ .

Input Format: The only line contains four integers $n$ , $l$ , $r$ , $z$ ( $1 \le n \le 1000$ , $1\le l\le r\le 10^{18}$ , $1\le z\le 10^{18}$ ).

Output Format: Print the number of arrays $a$ satisfying all requirements modulo $10^9+7$ .

Note: The following arrays satisfy the conditions for the first sample:

$[1, 0, 0]$ ;
$[0, 1, 0]$ ;
$[3, 2, 0]$ ;
$[2, 3, 0]$ ;
$[0, 0, 1]$ ;
$[1, 1, 1]$ ;
$[2, 2, 1]$ ;
$[3, 0, 2]$ ;
$[2, 1, 2]$ ;
$[1, 2, 2]$ ;
$[0, 3, 2]$ ;
$[2, 0, 3]$ ;
$[0, 2, 3]$ .

The following arrays satisfy the conditions for the second sample:

$[2, 0, 0, 0]$ ;
$[0, 2, 0, 0]$ ;
$[0, 0, 2, 0]$ ;
$[0, 0, 0, 2]$ .

1670F · Jee, You See?