Manasva "JARVIS" Katyal is going on an adventure in his beloved Grob 120A. There are destinations connected by
routes. The
th route connects destination
with destination
, using up
units of fuel. Routes can be flown both ways and multiple times. It is possible to reach every destination from every other destination using these routes. Since Manasva spent his life savings buying the Grob 120A, he's being really frugal and wants to save fuel. He asks
questions. For each question, he asks if it would be possible to fly from destination
to
while using exactly
units of fuel.
Constraints
Subtask 1 [40%]
Subtask 2 [60%]
Input Specification
The first line contains space-separated integers,
and
.
The next lines each contain
space-separated integers,
,
, and
, indicating a route connecting destination
with destination
which uses
units of fuel.
The next lines each contain
space-separated integers,
and
.
Output Specification
For each query, output a single line containing YES
if there exists a path and NO
if there is no valid path.
Sample Input
5 4
2 1 9
1 4 4
2 5 11
3 1 6
3 24
1 17
3 21
2 47
Sample Output
YES
NO
NO
YES
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