Bob has a connected undirected edge-weighted graph with vertices and
edges. There are no self-loops in this graph, but there can be multiple edges between some pairs of vertices.
Alice told Bob the following about this graph:
- The edge weights are distinct integers from the range
. In other words, they form some permutation of integers from
to
.
- The weight of the
-th edge is from the range
for each
from
to
.
- The edges with indices
(the first
edges in the input) form a minimum spanning tree of this graph.
Bob wants to know if it is possible. Determine if there exist such assignments of edge weights for which these conditions hold and if yes, find any of them.
Input Format
The first line contains a single integer (
), the number of test cases. The description of test cases follows.
The first line of each test case contains two integers and
(
), the number of vertices and the number of edges, respectively.
The -th of the following
lines contains four integers
,
,
,
(
,
), indicating that there is an edge connecting vertices
,
, and that its weight should be in range
.
It's guaranteed that for each test case, edges with indices form a spanning tree of the given graph.
It's guaranteed the sum of over all test cases doesn't exceed
.
Output Format
For each test case, if an array of edge weights that satisfy the conditions doesn't exist, output NO
in the first line.
Otherwise, in the first line, output YES
. In the second line output integers
(
, all
are distinct), the edge weights (where
is the weight assigned to the
-th edge in the input).
If there are multiple answers, output any of them.
Constraints
Subtask | Points | Additional constraints |
---|---|---|
The sum of | ||
The sum of | ||
The sum of | ||
The sum of | ||
No additional constraints |
Sample Input
3
4 6
1 2 1 3
1 3 2 6
3 4 1 2
1 4 2 5
2 3 2 4
2 4 4 6
4 4
1 2 2 2
2 3 3 3
3 4 4 4
1 4 1 4
5 6
1 2 1 1
2 3 1 2
3 4 2 4
4 5 6 6
1 4 4 6
1 4 5 6
Sample Output
YES
2 3 1 5 4 6
NO
YES
1 2 3 6 4 5
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