[USACO 2012 Jan G]Bovine Alliance
题号:NC24208
时间限制:C/C++/Rust/Pascal 1秒,其他语言2秒
空间限制:C/C++/Rust/Pascal 32 M,其他语言64 M
64bit IO Format: %lld

题目描述

Bessie and her bovine pals from nearby farms have finally decided that they are going to start connecting their farms together by trails in an effort to form an alliance against the farmers. The cows in each of the N (1 <= N <= 100,000) farms were initially instructed to build a trail to exactly one other farm, for a total of N trails. However months into the project only M (1 <= M < N) of these trails had actually been built. 
Arguments between the farms over which farms already built a trail now threaten to split apart the cow alliance. To ease tension, Bessie wishes to calculate how many ways the M trails that exist so far could have been built. For example, if there is a trail connecting farms 3 and 4, then one possibility is that farm 3 built the trail, and the other possibility is that farm 4 built the trail. Help Bessie by calculating the number of different assignments of trails to the farms that built them, modulo 1,000,000,007. Two assignments are considered different if there is at least one trail built by a different farm in each assignment.

输入描述:

* Line 1: Two space-separated integers N and M

* Lines 2..1+M: Line i+1 describes the ith trail. Each line contains
two space-separated integers u_i and v_i (1 <= u_i, v_i <= N,
u_i != v_i) describing the pair of farms connected by the
trail.

输出描述:

* Line 1: A single line containing the number of assignments of trails
to farms, taken modulo 1,000,000,007. If no assignment
satisfies the above conditions output 0.
示例1

输入

复制
5 4
1 2
3 2
4 5
4 5

输出

复制
6

说明

There are 6 possible assignments.  Letting {a,b,c,d} mean that farm 1
builds trail a, farm 2 builds trail b, farm 3 builds trail c, and farm 4
builds trail d, the assignments are:
{2, 3, 4, 5}
{2, 3, 5, 4}
{1, 3, 4, 5}
{1, 3, 5, 4}
{1, 2, 4, 5}
{1, 2, 5, 4}

备注:

Note that there can be two trails between the same pair of farms.