Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Festival Organization

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Prodiggers are quite a cool band and for this reason, they have been the surprise guest at the ENTER festival for the past 80 years. At the beginning of their careers, they weren’t so successful, so they had to spend time digging channels to earn money; hence the name. Anyway, they like to tour a lot and have surprising amounts of energy to do extremely long tours. However, they hate spending two consecutive days without having a concert, so they would like to avoid it.

A tour is defined by a sequence of concerts and days-off. You need to count in how many ways The Prodiggers can select *k* different tours of the same length between *l* and *r*.

For example if *k* = 2, *l* = 1 and *r* = 2, if we define concert day as {1} and day-off as {0}, here are all possible tours: {0}, {1}, {00}, {01}, {10}, {11}. But tour 00 can not be selected because it has 2 days-off in a row. Now, we need to count in how many ways we can select *k* = 2 tours of the same length in range [1;2]. Here they are: {0,1}; {01,10}; {01,11}; {10,11}.

Since their schedule is quite busy, they want you to tell them in how many ways can do that, modulo 1 000 000 007 (10^{9} + 7).

Input

The first line of the input contains three integers *k*, *l* and *r* (1 ≤ *k* ≤ 200, 1 ≤ *l* ≤ *r* ≤ 10^{18}).

Output

Output a single number: the number of ways to select *k* different tours of the same length, modulo 1 000 000 007.

Example

Input

1 1 2

Output

5

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/24/2020 05:52:11 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|