Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-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

D. Airplane Arrangements

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere is an airplane which has *n* rows from front to back. There will be *m* people boarding this airplane.

This airplane has an entrance at the very front and very back of the plane.

Each person has some assigned seat. It is possible for multiple people to have the same assigned seat. The people will then board the plane one by one starting with person 1. Each person can independently choose either the front entrance or back entrance to enter the plane.

When a person walks into the plane, they walk directly to their assigned seat and will try to sit in it. If it is occupied, they will continue walking in the direction they walked in until they are at empty seat - they will take the earliest empty seat that they can find. If they get to the end of the row without finding a seat, they will be angry.

Find the number of ways to assign tickets to the passengers and board the plane without anyone getting angry. Two ways are different if there exists a passenger who chose a different entrance in both ways, or the assigned seat is different. Print this count modulo 10^{9} + 7.

Input

The first line of input will contain two integers *n*, *m* (1 ≤ *m* ≤ *n* ≤ 1 000 000), the number of seats, and the number of passengers, respectively.

Output

Print a single number, the number of ways, modulo 10^{9} + 7.

Example

Input

3 3

Output

128

Note

Here, we will denote a passenger by which seat they were assigned, and which side they came from (either "F" or "B" for front or back, respectively).

For example, one valid way is 3B, 3B, 3B (i.e. all passengers were assigned seat 3 and came from the back entrance). Another valid way would be 2F, 1B, 3F.

One invalid way would be 2B, 2B, 2B, since the third passenger would get to the front without finding a seat.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/22/2019 20:25:20 (d3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|