5068: Duff in Mafia
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：2
通过：1
题目描述
D. Duff in Mafia
time limit per test
6 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Duff is one if the heads of Mafia in her country, Andarz Gu. Andarz Gu has n cities (numbered from 1 to n) connected by m bidirectional roads (numbered by 1 to m).
Each road has a destructing time, and a color. i-th road connects cities vi and ui and its color is ci and its destructing time is ti.
Mafia wants to destruct a matching in Andarz Gu. A matching is a subset of roads such that no two roads in this subset has common endpoint. They can destruct these roads in parallel, i. e. the total destruction time is a maximum over destruction times of all selected roads.
They want two conditions to be satisfied:
There is no programmer in Mafia. That's why Duff asked for your help. Please help her and determine which matching to destruct in order to satisfied those conditions (or state that this is not possible).
Each road has a destructing time, and a color. i-th road connects cities vi and ui and its color is ci and its destructing time is ti.
Mafia wants to destruct a matching in Andarz Gu. A matching is a subset of roads such that no two roads in this subset has common endpoint. They can destruct these roads in parallel, i. e. the total destruction time is a maximum over destruction times of all selected roads.
They want two conditions to be satisfied: - The remaining roads form a proper coloring.
- Destructing time of this matching is minimized.
There is no programmer in Mafia. That's why Duff asked for your help. Please help her and determine which matching to destruct in order to satisfied those conditions (or state that this is not possible).
Input
The first line of input contains two integers n and m (2≤n≤5×104 and 1≤m≤5×104), number of cities and number of roads in the country. The next m lines contain the the roads. i-th of them contains four integers vi,ui,ci and ti (1≤vi,ui≤n, vi≠ui and 1≤ci,ti≤109 for each 1≤i≤m).
Output
In the first line of input, print "Yes" (without quotes) if satisfying the first condition is possible and "No" (without quotes) otherwise. If it is possible, then you have to print two integers t and k in the second line, the minimum destructing time and the number of roads in the matching (
). In the third line print k distinct integers separated by spaces, indices of the roads in the matching in any order. Roads are numbered starting from one in order of their appearance in the input.
If there's more than one solution, print any of them.
Examples
Input
5 7 2 1 3 7 3 1 1 6 5 4 1 8 4 5 1 1 3 2 2 3 4 5 2 5 2 3 2 4
Output
Yes 3 2 4 5
Input
3 5 3 2 1 3 1 3 1 1 3 2 1 4 1 3 2 2 1 3 2 10
Output
No
Note
Graph of Andarz Gu in the first sample case is as follows: 
A solution would be to destruct the roads with crosses. Graph of Andarz Gu in the second sample case is as follows:
输入样例 复制
输出样例 复制