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 $10^9+7$.

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

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