mod util {
    pub trait Join {
        fn join(self, sep: &str) -> String;
    }

    impl<T, I> Join for I
    where
        I: Iterator<Item = T>,
        T: std::fmt::Display,
    {
        fn join(self, sep: &str) -> String {
            let mut s = String::new();
            use std::fmt::*;
            for (i, v) in self.enumerate() {
                if i > 0 {
                    write!(&mut s, "{}", sep).ok();
                }
                write!(&mut s, "{}", v).ok();
            }
            s
        }
    }
}
// ---------- begin chmin, chmax ----------
pub trait ChangeMinMax {
    fn chmin(&mut self, x: Self) -> bool;
    fn chmax(&mut self, x: Self) -> bool;
}

impl<T: PartialOrd> ChangeMinMax for T {
    fn chmin(&mut self, x: Self) -> bool {
        *self > x && {
            *self = x;
            true
        }
    }
    fn chmax(&mut self, x: Self) -> bool {
        *self < x && {
            *self = x;
            true
        }
    }
}
// ---------- end chmin, chmax ----------
// ---------- begin quick find ----------
pub struct QuickFind {
    size: usize,
    id: Vec<usize>,
    list: Vec<Vec<usize>>,
}

impl QuickFind {
    pub fn new(size: usize) -> Self {
        let id = (0..size).collect::<Vec<_>>();
        let list = (0..size).map(|x| vec![x]).collect::<Vec<_>>();
        QuickFind { size, id, list }
    }
    pub fn root(&self, x: usize) -> usize {
        assert!(x < self.size);
        self.id[x]
    }
    pub fn same(&self, x: usize, y: usize) -> bool {
        assert!(x < self.size);
        assert!(y < self.size);
        self.root(x) == self.root(y)
    }
    pub fn unite(&mut self, x: usize, y: usize) -> Option<(usize, usize)> {
        assert!(x < self.size);
        assert!(y < self.size);
        let mut x = self.root(x);
        let mut y = self.root(y);
        if x == y {
            return None;
        }
        if (self.list[x].len(), x) < (self.list[y].len(), y) {
            std::mem::swap(&mut x, &mut y);
        }
        let mut z = std::mem::take(&mut self.list[y]);
        z.iter().for_each(|y| self.id[*y] = x);
        self.list[x].append(&mut z);
        Some((x, y))
    }
    pub fn enumerate(&self, x: usize) -> &[usize] {
        assert!(x < self.size);
        &self.list[self.root(x)]
    }
    pub fn size(&self, x: usize) -> usize {
        assert!(x < self.size);
        self.enumerate(x).len()
    }
}
// ---------- end quick find ----------
// ---------- begin scannner ----------
#[allow(dead_code)]
mod scanner {
    use std::str::FromStr;
    pub struct Scanner<'a> {
        it: std::str::SplitWhitespace<'a>,
    }
    impl<'a> Scanner<'a> {
        pub fn new(s: &'a String) -> Scanner<'a> {
            Scanner {
                it: s.split_whitespace(),
            }
        }
        pub fn next<T: FromStr>(&mut self) -> T {
            self.it.next().unwrap().parse::<T>().ok().unwrap()
        }
        pub fn next_bytes(&mut self) -> Vec<u8> {
            self.it.next().unwrap().bytes().collect()
        }
        pub fn next_chars(&mut self) -> Vec<char> {
            self.it.next().unwrap().chars().collect()
        }
        pub fn next_vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
            (0..len).map(|_| self.next()).collect()
        }
    }
}
// ---------- end scannner ----------

use std::collections::*;
use std::io::Write;

type Map<K, V> = BTreeMap<K, V>;
type Set<T> = BTreeSet<T>;
type Deque<T> = VecDeque<T>;

fn main() {
    use std::io::Read;
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut sc = scanner::Scanner::new(&s);
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    run(&mut sc, &mut out);
}

fn run<W: Write>(sc: &mut scanner::Scanner, out: &mut std::io::BufWriter<W>) {
    let t: u32 = sc.next();
    for _ in 0..t {
        let n: usize = sc.next();
        let m: usize = sc.next();
        let mut e = vec![(0, 0); m];
        let mut test = QuickFind::new(n);
        for e in e.iter_mut() {
            e.0 = sc.next::<usize>() - 1;
            e.1 = sc.next::<usize>() - 1;
            test.unite(e.0, e.1);
        }
        let a: Vec<usize> = sc.next_vec(n);
        if test.size(0) != n {
            writeln!(out, "No").ok();
            continue;
        }
        let mut g = vec![vec![]; n];
        for (i, &(a, b)) in e.iter().enumerate() {
            g[a].push((b, i));
            g[b].push((a, i));
        }
        let mut ord = vec![n; n];
        let mut low = vec![n; n];
        let mut id = 0;
        dfs(0, m, &g, &mut ord, &mut low, &mut id);
        let mut dsu = QuickFind::new(n);
        for (x, y) in ord.iter().zip(low.iter()) {
            dsu.unite(*x, *y);
        }
        drop(g);
        drop(ord);
        drop(low);
        let vertex = (0..n).filter(|v| *v == dsu.root(*v)).collect::<Vec<_>>();
        let mut tree = vec![vec![]; vertex.len()];
        for &(a, b) in e.iter() {
            if dsu.root(a) != dsu.root(b) {
                let a = vertex.binary_search(&dsu.root(a)).unwrap();
                let b = vertex.binary_search(&dsu.root(b)).unwrap();
                tree[a].push(b);
                tree[b].push(a);
            }
        }
        let g = tree;
        let mut hist = vec![0; n + 1];
        for a in a.iter() {
            hist[*a] += 1;
        }
        hist.retain(|h| *h > 0);
        hist.insert(0, 0);
        for i in 1..hist.len() {
            hist[i] += hist[i - 1];
        }
        let mut z = a.clone();
        z.sort();
        z.dedup();
        let (hist, z) = (hist, z);
        let mut inv = vec![None; n + 1];
        for i in 1..hist.len() {
            inv[hist[i]] = Some(i);
        }
        let mut topo = vec![0];
        let mut parent = vec![None; g.len()];
        for i in 0..g.len() {
            let v = topo[i];
            for u in g[v].clone() {
                if Some(u) != parent[v] {
                    topo.push(u);
                    parent[u] = Some(v);
                }
            }
        }
        let (parent, topo) = (parent, topo);
        let mut dp = vec![0; g.len()];
        let mut size = vertex.iter().map(|v| dsu.size(*v)).collect::<Vec<_>>();
        for &v in topo.iter().rev() {
            let mut val = 0;
            for &u in g[v].iter() {
                if parent[v] == Some(u) {
                    continue;
                }
                val = val.max(dp[u]);
                if let Some(k) = inv[size[u]] {
                    if dp[u] == k - 1 {
                        val = val.max(k);
                    }
                }
                size[v] += size[u];
            }
            dp[v] = val;
        }
        let mut up = vec![0; g.len()];
        for &v in topo.iter() {
            let mut child = g[v].clone();
            child.retain(|c| parent[*c] == Some(v));
            let mut val = up[v];
            let mut memo = vec![val];
            for &u in child.iter() {
                val.chmax(dp[u]);
                if let Some(k) = inv[size[u]] {
                    if dp[u] == k - 1 {
                        val = val.max(k);
                    }
                }
                memo.push(val);
            }
            let left = memo;
            let mut val = up[v];
            let mut memo = vec![val];
            for &u in child.iter().rev() {
                val.chmax(dp[u]);
                if let Some(k) = inv[size[u]] {
                    if dp[u] == k - 1 {
                        val = val.max(k);
                    }
                }
                memo.push(val);
            }
            let right = memo;
            for (i, &u) in child.iter().enumerate() {
                let mut val = left[i].max(right[right.len() - 2 - i]);
                if let Some(k) = inv[n - size[u]] {
                    if val == k - 1 {
                        val = k;
                    }
                }
                up[u] = val;
            }
        }
        let mut v = vertex.len();
        for i in 0..g.len() {
            if dp[i] == z.len() - 1 || up[i] == z.len() - 1 {
                v = i;
            }
        }
        if v == vertex.len() {
            writeln!(out, "No").ok();
            continue;
        }
        let root = v;
        let mut g = g;
        let mut topo = vec![root];
        for i in 0..g.len() {
            let v = topo[i];
            for u in g[v].clone() {
                g[u].retain(|p| *p != v);
                topo.push(u);
            }
        }
        let mut size = vertex.iter().map(|v| dsu.size(*v)).collect::<Vec<_>>();
        for &v in topo.iter().rev() {
            let mut val = 0;
            for &u in g[v].iter() {
                val = val.max(dp[u]);
                if let Some(k) = inv[size[u]] {
                    if dp[u] == k - 1 {
                        val = val.max(k);
                    }
                }
                size[v] += size[u];
            }
            dp[v] = val;
        }
        let mut del = Map::new();
        let mut pos = root;
        while dp[pos] > 0 {
            let mut update = false;
            for &u in g[pos].iter() {
                if dp[u] == dp[pos] {
                    pos = u;
                    update = true;
                    break;
                } else if inv[size[u]].map_or(false, |k| dp[u] == k - 1 && dp[pos] == k) {
                    del.insert((pos, u), dp[pos]);
                    pos = u;
                    update = true;
                    break;
                }
            }
            assert!(update);
        }
        let mut value = vec![z[0]; n];
        let mut add = vec![];
        for &(a, b) in e.iter() {
            if dsu.same(a, b) {
                continue;
            }
            let x = dsu.root(a);
            let y = dsu.root(b);
            let s = vertex.binary_search(&x).unwrap();
            let t = vertex.binary_search(&y).unwrap();
            let mut update = false;
            if let Some(&v) = del.get(&(s, t)) {
                value[x] = z[v];
                update = true;
            }
            if let Some(&v) = del.get(&(t, s)) {
                value[y] = z[v];
                update = true;
            }
            if !update {
                add.push((x, y));
            }
        }
        for (a, b) in add {
            let (p, c) = dsu.unite(a, b).unwrap();
            if value[c] != z[0] {
                value[p] = value[c];
            }
        }
        writeln!(out, "Yes").ok();
        use util::*;
        writeln!(out, "{}", (0..n).map(|v| value[dsu.root(v)]).join(" ")).ok();
    }
}

fn dfs(
    v: usize,
    prev: usize,
    g: &[Vec<(usize, usize)>],
    ord: &mut [usize],
    low: &mut [usize],
    id: &mut usize,
) {
    ord[v] = *id;
    low[v] = *id;
    *id += 1;
    for &(u, k) in g[v].iter().filter(|e| e.1 != prev) {
        if ord[u] > *id {
            dfs(u, k, g, ord, low, id);
            low[v] = low[v].min(low[u]);
        } else {
            low[v] = low[v].min(ord[u]);
        }
    }
}