Input 
5 5 13 0 4
0 1 5
2 1 2
3 2 3
1 4 0
4 3 4
Output 
YES
0 1 5
2 1 2
3 2 3
1 4 8
4 3 4
Input 
2 1 123456789 0 1
0 1 0
Output 
YES
0 1 123456789
Input 
2 1 999999999 1 0
0 1 1000000000
Output 
NO