MST Edge Check

Given an undirected weighted graph, determine for each edge if it can be included in a minimum spanning tree.

Input

The first line has two integers n and m: the number of nodes and edges. The nodes are numbered 1,2,\dots,n. The following m lines describe the edges. Each line has three integers a, b, w: there is an edge between nodes a and b with weight w. You can assume that the graph is connected and simple and each edge appears at most once in the graph.

Output

For each edge in the input order, print YES if it can be included in the minimum spanning tree and NO otherwise.

Constraints

$1 \le n \le 10^5$

$1 \le m \le 2$ \cdot 10^5$

$1 \le a,b \le n$

$1 \le w \le 10^9$

Example

Input

5 6
1 2 4
1 3 2
2 4 2
3 4 1
3 5 3
4 5 3

Output

NO
YES
YES
YES
YES
YES