'Twas the night before Christmas, and Santa's frantically setting up his new Christmas tree! There are n nodes in the tree, connected by n-1 edges. On each edge of the tree, there's a set of Christmas lights, which can be represented by an integer in binary representation.

<image>

He has m elves come over and admire his tree. Each elf is assigned two nodes, a and b, and that elf looks at all lights on the simple path between the two nodes. After this, the elf's favorite number becomes the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of the values of the lights on the edges in that path.

However, the North Pole has been recovering from a nasty bout of flu. Because of this, Santa forgot some of the configurations of lights he had put on the tree, and he has already left the North Pole! Fortunately, the elves came to the rescue, and each one told Santa what pair of nodes he was assigned (a_i, b_i), as well as the parity of the number of set bits in his favorite number. In other words, he remembers whether the number of 1's when his favorite number is written in binary is odd or even.

Help Santa determine if it's possible that the memories are consistent, and if it is, remember what his tree looked like, and maybe you'll go down in history!

Input

The first line contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t cases follow.

The first line of each test case contains two integers, n and m (2 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ m ≤ 2 ⋅ 10^5) — the size of tree and the number of elves respectively.

The next n-1 lines of each test case each contains three integers, x, y, and v (1 ≤ x, y ≤ n; -1 ≤ v < 2^{30}) — meaning that there's an edge between nodes x and y. If 

  * v = -1: Santa doesn't remember what the set of lights were on for this edge. 
  * v ≥ 0: The set of lights on the edge is v. 



The next m lines of each test case each contains three integers, a, b, and p (1 ≤ a, b ≤ n; a ≠ b; 0 ≤ p ≤ 1) — the nodes that the elf was assigned to, and the parity of the number of set bits in the elf's favorite number.

It is guaranteed that the sum of all n and the sum of all m don't exceed 2 ⋅ 10^5 each.

It is guaranteed that the given edges form a tree.

Output

For each test case, first print either YES or NO (in any case), whether there's a tree consistent with Santa's memory or not. 

If the answer is YES, print n-1 lines each containing three integers: x, y, and v (1 ≤ x, y ≤ n; 0 ≤ v < 2^{30}) — the edge and the integer on that edge. The set of edges must be the same as in the input, and if the value of some edge was specified earlier, it can not change. You can print the edges in any order.

If there are multiple answers, print any.

Example

Input


4
6 5
1 2 -1
1 3 1
4 2 7
6 3 0
2 5 -1
2 3 1
2 5 0
5 6 1
6 1 1
4 5 1
5 3
1 2 -1
1 3 -1
1 4 1
4 5 -1
2 4 0
3 4 1
2 3 1
3 3
1 2 -1
1 3 -1
1 2 0
1 3 1
2 3 0
2 1
1 2 1
1 2 0


Output


YES
1 2 0
1 3 1
2 4 7
3 6 0
2 5 0
YES
1 2 1
1 3 0
1 4 1
4 5 1
NO
NO

Note

The first test case is the image in the statement.

One possible answer is assigning the value of the edge (1, 2) to 5, and the value of the edge (2, 5) to 3. This is correct because: 

  * The first elf goes from node 2 to node 3. This elf's favorite number is 4, so he remembers the value 1 (as 4 has an odd number of 1 bits in its binary representation). 
  * The second elf goes from node 2 to node 5. This elf's favorite number is 3, so he remembers the value 0 (as 3 has an even number of 1 bits in its binary representation). 
  * The third elf goes from node 5 to node 6. This elf's favorite number is 7, so he remembers the value 1 (as 7 has an odd number of 1 bits in its binary representation). 
  * The fourth elf goes from node 6 to node 1. This elf's favorite number is 1, so he remembers the value 1 (as 1 has an odd number of 1 bits in its binary representation). 
  * The fifth elf goes from node 4 to node 5. This elf's favorite number is 4, so he remembers the number 1 (as 4 has an odd number of 1 bits in its binary representation). 



Note that there are other possible answers.
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
using pcc = pair<char, char>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tuplis = array<ll, 3>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const int MOD=1000000007;
const int MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.1415926535897932;
const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1};
const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1};
#define overload5(a,b,c,d,e,name,...) name
#define overload4(a,b,c,d,name,...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i=n;i--;)
#define rrep2(i,n) for(ll i=n;i--;)
#define rrep3(i,a,b) for(ll i=b;i-->(a);)
#define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c)
#define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define each1(i,a) for(auto&&i:a)
#define each2(x,y,a) for(auto&&[x,y]:a)
#define each3(x,y,z,a) for(auto&&[x,y,z]:a)
#define each4(w,x,y,z,a) for(auto&&[w,x,y,z]:a)
#define each(...) overload5(__VA_ARGS__,each4,each3,each2,each1)(__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(),(i).rend()
#define rall2(i,k) (i).rbegin(),(i).rbegin()+k
#define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__),0.0L)
#define Msum(...) accumulate(all(__VA_ARGS__),0_M)
#define elif else if
#define unless(a) if(!(a))
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define vec(type,name,...) vector<type>name(__VA_ARGS__)
#define VEC(type,name,size) vector<type>name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
template<class T, class U> auto count(const T& a, const U& b){ return count(all(a), b); }
template<class T, class U> auto count_if(const T& a, U b){ return count_if(all(a), b); }
inline ll popcnt(ull a){ return __builtin_popcountll(a); }
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T> bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; }
template<class T, class U> bool chmin(T& a, const U& b){ if(a > T(b)){ a = b; return 1; } return 0; }
template<class T, class U> bool chmax(T& a, const U& b){ if(a < T(b)){ a = b; return 1; } return 0; }
vector<ll> iota(ll n, ll begin = 0){ vector<ll> a(n); iota(a.begin(), a.end(), begin); return a; }
vector<pll> factor(ull x){ vector<pll> ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; }
vector<ll> divisor(ull x){ vector<ll> ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; }
template<class T> unordered_map<T, ll> press(vector<T> a){ Uniq(a); unordered_map<T, ll> ans; rep(a.size()) ans[a[i]] = i; return ans; }
template<class T> auto run_press(const T& a){ vector<pair<remove_const_t<remove_reference_t<decltype(a[0])>>, ll>> ans; each(x, a){ if(ans.empty() || ans.back().first != x) ans.emplace_back(x, 1); else ans.back().second++; } return ans; }
int scan(){ return getchar(); }
void scan(int& a){ scanf("%d", &a); }
void scan(unsigned& a){ scanf("%u", &a); }
void scan(long& a){ scanf("%ld", &a); }
void scan(long long& a){ scanf("%lld", &a); }
void scan(unsigned long long& a){ scanf("%llu", &a); }
void scan(char& a){ do a = getchar(); while(a == ' ' || a == '\n'); }
void scan(float& a){ scanf("%f", &a); }
void scan(double& a){ scanf("%lf", &a); }
void scan(long double& a){ scanf("%Lf", &a); }
void scan(vector<bool>& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } }
void scan(char a[]){ scanf("%s", a); }
void scan(string& a){ cin >> a; }
template<class T> void scan(vector<T>&);
template<class T, size_t size> void scan(array<T, size>&);
template<class T, class L> void scan(pair<T, L>&);
template<class T, size_t size> void scan(T(&)[size]);
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
template<class T> void scan(deque<T>& a){ for(auto&& i : a) scan(i); }
template<class T, size_t size> void scan(array<T, size>& a){ for(auto&& i : a) scan(i); }
template<class T, class L> void scan(pair<T, L>& p){ scan(p.first); scan(p.second); }
template<class T, size_t size> void scan(T (&a)[size]){ for(auto&& i : a) scan(i); }
template<class T> void scan(T& a){ cin >> a; }
void in(){}
template <class... T> void in(T&... a){ (void)initializer_list<int>{ (scan(a), 0)... }; }
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(unsigned a){ printf("%u", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(unsigned long long a){ printf("%llu", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(float a){ printf("%.15f", a); }
void print(double a){ printf("%.15f", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
template<class T> void print(const complex<T>& a){ if(a.real() >= 0) print('+'); print(a.real()); if(a.imag() >= 0) print('+'); print(a.imag()); print('i'); }
template<class T> void print(const vector<T>&);
template<class T, size_t size> void print(const array<T, size>&);
template<class T, class L> void print(const pair<T, L>& p);
template<class T, size_t size> void print(const T (&)[size]);
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size>& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L>& p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
inline ll __lg(ull x){ return 63 - __builtin_clzll(x); }
#define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...) void(0)
#endif
int first(bool i = true){ return out(i?"first":"second"); }
int First(bool i = true){ return out(i?"First":"Second"); }
int yes(bool i = true){ return out(i?"yes":"no"); }
int Yes(bool i = true){ return out(i?"Yes":"No"); }
int No(){ return out("No"); }
int YES(bool i = true){ return out(i?"YES":"NO"); }
int NO(){ return out("NO"); }
int Yay(bool i = true){ return out(i?"Yay!":":("); }
int possible(bool i = true){ return out(i?"possible":"impossible"); }
int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
void Case(ll i){ printf("Case #%lld: ", i); }


struct UnionFind{
    vector<ll> data;
    UnionFind(ll n): data(n, -1){}
    bool unite(ll a, ll b){
        a = root(a); b = root(b);
        if(a == b) return 0;
        if(data[a] > data[b]) swap(a, b);
        data[a] += data[b];
        data[b] = a;
        return 1;
    }
    bool find(ll a, ll b){ return root(a) == root(b); }
    ll root(ll a){ return data[a] < 0 ? a : data[a] = root(data[a]); }
    ll size(ll a){ return -data[root(a)]; }
    ll operator[](ll a){ return root(a); }
};
void solve(){
    LL(n,m);
    VEC(tuplis,edge,n-1);
    UnionFind uf(n*2);
    each(a,b,c,edge){
        a--; b--;
        if(c!=-1){
            if(__builtin_parityll(c)){
                uf.unite(a,b+n);
                uf.unite(b,a+n);
            }
            else{
                uf.unite(a,b);
                uf.unite(a+n,b+n);
            }
        }
    }
    rep(m){
        LL(a,b,p);
        a--; b--;
        if(p){
            uf.unite(a,b+n);
            uf.unite(b,a+n);
        }
        else{
            uf.unite(a,b);
            uf.unite(a+n,b+n);
        }
    }
    rep(n)if(uf.find(i,i+n))return(void)NO();
    YES();
    rep(n-1)if(uf.find(i,i+1)&&uf.find(i,i+1+n)){
        uf.unite(i,i+1);
        uf.unite(i+n,i+1+n);
    }
    each(a,b,c,edge)if(c==-1)c=uf.find(a,b+n);
    each(i,edge)out(i);
}
int main(){
    LL(t);
    rep(t)solve();
}