194. Reactor Cooling
time limit per test: 0.5
sec.
memory limit per test: 65536
KB
input: standard
output: standard
The terrorist group leaded by a well known international terrorist Ben Bladen is buliding a nuclear reactor to produce plutonium for the nuclear bomb they are planning to create. Being the wicked computer genius of this group, you are responsible for developing the cooling system for the reactor.
The cooling system of the reactor consists of the number of pipes that special cooling liquid flows by. Pipes are connected at special points, called nodes, each pipe has the starting node and the end point. The liquid must flow by the pipe from its start point to its end point and not in the opposite direction.
Let the nodes be numbered from 1 to N. The cooling system must be designed so that the liquid is circulating by the pipes and the amount of the liquid coming to each node (in the unit of time) is equal to the amount of liquid leaving the node. That is, if we designate the amount of liquid going by the pipe from ith node to jth as f_{ij}, (put f_{ij} = 0 if there is no pipe from node i to node j), for each i the following condition must hold:
sum(j=1..N, f_{ij}) = sum(j=1..N, f_{ji})
Each pipe has some finite capacity, therefore for each i and j connected by the pipe must be f_{ij} ≤ c_{ij} where c_{ij} is the capacity of the pipe. To provide sufficient cooling, the amount of the liquid flowing by the pipe going from ith to jth nodes must be at least l_{ij}, thus it must be f_{ij} ≥ l_{ij}.
Given c_{ij} and l_{ij} for all pipes, find the amount f_{ij}, satisfying the conditions specified above.
Input
The first line of the input file contains the number N (1 ≤ N ≤ 200)  the number of nodes and and M — the number of pipes. The following M lines contain four integer number each  i, j, l_{ij} and c_{ij} each. There is at most one pipe connecting any two nodes and 0 ≤ l_{ij} ≤ c_{ij} ≤ 10^{5} for all pipes. No pipe connects a node to itself. If there is a pipe from ith node to jth, there is no pipe from jth node to ith.
Output
On the first line of the output file print YES if there is the way to carry out reactor cooling and NO if there is none. In the first case M integers must follow, kth number being the amount of liquid flowing by the kth pipe. Pipes are numbered as they are given in the input file.
Sample test(s)
Input
Test #1
4 6
1 2 1 2
2 3 1 2
3 4 1 2
4 1 1 2
1 3 1 2
4 2 1 2
Test #2
4 6
1 2 1 3
2 3 1 3
3 4 1 3
4 1 1 3
1 3 1 3
4 2 1 3
Output
Test #1
NO
Test #2
YES
1
2
3
2
1
1
Author:  Andrew Stankevich

Resource:  Petrozavodsk Winter Trainings 2003

Date:  20030206

Server time: 20160925 00:50:42  Online Contester Team © 2002  2016. All rights reserved. 

