AKBAR  Akbar , The great
All of us are familiar with the reign of the great mughal ruler , Akbar. He was always concerned with the prosperity and safety of the people . Therefore to safeguard his kingdom (which consisted of N cities) he wanted to place secret soldiers all over his kingdom so as to protect the people . But since his kingdom is very large therefore he wanted to place them in such a way that every city is protected by one and only one soldier.According to Akbar , this is the optimum placement.
As for these soldiers they can protect multiple cities according to their strengths.
The strength of a particular soldier is defined as the maximum distance upto which a guard can protect a city from its base city(base city is the city assigned to the guard). If there are 3 cities C1, C2 and C3 such that C1 C2 and C2 C3 are connected respectively, if a soldier with strength 1 is placed at C2 then all the cities C1, C2 and C3 are protected by that soldier.
Also the kingdom is connected with a network of secret two way roads for faster access only accessible to these soldiers. The length of any road on this network between any two cities is 1 kms .There are R such roads in the kingdom.
He had given this task to birbal to place the soldiers . Birbal didn't wanted to be a fool in front of the king , therefore took the job and placed M soldiers all over the kingdom but he was not very good at mathematics . But since he is very intelligent he somehow places the guards all over the kingdom and now turns to you (who is a genius mathematician ;) ) to check whether his placements are good or not.
Your task is to check if the placements of the soldiers are optimum or not.
INPUT
The input consists of T test cases . Each test case then consists of 3 parts.The first line consists of N, R and M.
the next R lines consists of two numbers A and B denoting the two cities between which a road exists .
the next M lines consists of 2 numbers, city number K and strength S of that particular soldier.
=> strength 0 means it will only guard the city on which it is present .
=> assume every city is accesible from every other city .
CONSTRAINTS
T <= 10;
1 <= N <= 10^6;
N 1 <= R <= min( 10^7 , ( N * (N  1) ) / 2) );
1 <= K <= N;
0 <= S <= 10^6
OUTPUT
print "Yes" if the soldiers are placed optimumly else print "No". (quotes are for clarity)
SAMPLE INPUT
2
3 2 2
1 2
2 3
1 2
2 0
4 5 2
1 4
1 2
1 3
4 2
3 4
2 1
3 0
SAMPLE OUTPUT
No
Yes
WARNING ==> Large input.
hide comments
arnav7060:
20200916 18:25:23
got accepted in 18th try!!! A nice question took my whole day to solve it. 

nmnsharma007:
20200718 09:45:31
How to take care of cycles? 

tanayak:
20200712 03:21:49
Hello guys, I am pretty new to spoj and competitive programming, I am getting WA while submission


c_tycoon:
20200627 01:35:48
Please explain me the first test case . As 1 is connected to 2 ,2 to 3 . And 1 has soldier who can protect 3 and 2 has soldier who can protect 2 . Why it is No ? Or we should not have soldier in 2 as two can be saved by one's soldier


madina11906036:
20200606 17:05:43
cycle!!! 

nrg_sama:
20200519 21:51:25
Last edit: 20200519 23:40:21 

robosapien:
20200426 23:24:54
the question is framed in such a way that it might be confusing.


oneshott:
20200408 16:41:11
O(M*(V+E)) gives TLE where Vno.of vertices /Eno.of edges/Mno. of city point soldier strength


avik26091998:
20200320 09:08:34
Take care of cycle !!! 

tikli_10:
20200222 16:25:16
Please help, I have tried all test cases in the comments correctly, but still getting wrong answer on submission: 25439183 
Added by:  Prayank Mathur 
Date:  20141012 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  own 