Jee, You See? Codeforces Solution | Codeforces Problem Solution 2022

Jee, You See? Codeforces Solution | Codeforces Problem Solution 2022

F. Jee, You See?

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

Solution Click Below:-  CLICK HERE

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

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• 𝑙≤𝑎1+𝑎2+…+𝑎𝑛≤𝑟$l\le a_1+a_2+\dots +a_n\le r$, and
• 𝑎1⊕𝑎2⊕…⊕𝑎𝑛=𝑧$a_1\oplus a_2\oplus \dots \oplus a_n=z$, where ⊕$\oplus$ denotes the bitwise XOR operation.

Since the answer can be large, print it modulo 109+7${10}^9+7$.

Input

The only line contains four integers 𝑛$n$, 𝑙$l$, 𝑟$r$, 𝑧$z$ (1≤𝑛≤1000$1\le n\le 1000$, 1≤𝑙≤𝑟≤1018$1\le l\le r\le {10}^{18}$, 1≤𝑧≤1018$1\le z\le {10}^{18}$).

Output

Print the number of arrays 𝑎$a$ satisfying all requirements modulo 109+7${10}^9+7$.

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