Hi, Codeforces. I've recently found an interesting problem:

Given an undirected tree with n vertices. Find out how many different ways you can orient the edges of the tree so that the result graph will contain exactly m vertices with zero outdegree modulo 10⁹ + 7,   (1 ≤ n ≤ 1000, 0 ≤ m ≤ n).

Could someone help me with this problem and explain the solution?

Hello Codeforces!

On July 24, в 17:35 MSK rated Codeforces Round #425 (Div. 2) will be held. As always, participants from the first division can take part out of competition.

This is my first round. Many thanks to Nikolay Kalinin (KAN) and Alexey Ilyukhov (Livace) for help in preparations of the round, Ildar Gainullin (300iq), Daniil Nikolenko (qoo2p5) and AmirReza PoorAkhavan (Arpa) for testing problems and also to Mike Mirzayanov (MikeMirzayanov) for Codeforces and Polygon platforms.

You will be given 5 problems and 2 hours to solve them. Scoring will be announced before the round.

I hope you'll enjoy my round. I wish everyone good luck and high rating!

UPD1: The scoring for this round is: 500 — 1000 — 1750 — 2000 — 2500.

UPD2: Congratulations to the winners! Editorial here.

Div.2 :

1. LGTwins

2. nick452

3. Torta

4. ez_zjt

5. Parachutes

Div.1 :

1. TimonKnigge

2. Um_nik

3. quailty

4. dotorya

5. Kaban-5