Potential

You are given a weighted directed graph. Each vertex $i$ has a potential $\Phi_i$. Let $w_{uv}$ be the weight of the edge $(u, v)$. The new weight is defined as $w'_{uv} = w_{uv} + \Phi_u - \Phi_v$.

Find integer potentials $\Phi_i$ such that the new weights $w'$ of all edges are equal.

The first line of input contains an integer $t$, the number of test cases.

Each test case starts with a line containing two integers $n$ and $m$, the number of vertices and edges in the graph ($1 \le n \le 300\,000$, $0 \le m \le 300\,000$). Each of the next $m$ lines contains three integers $x_i$, $y_i$ and $w_i$, the start vertex, end vertex, and weight of an edge ($1 \le x_i, y_i \le n$, $-10^9 \le w_i \le 10^9$). The graph has no self-loops and no multiple edges.

The sum of all $n$ and the sum of all $m$ do not exceed $600\,000$.

For each test case, print "YES" on the first line if an integer solution exists, or "NO" otherwise.

If a solution exists, print $n$ integers on the next line: the potentials of the vertices. The absolute value of each potential must not exceed $10^{18}$. If a solution exists, one satisfying this bound is guaranteed to exist.

If there is more than one solution, print any one of them.