#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;
//#define int long long
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
//ll mod = 1;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const int mod17 = 1000000007;
const ll INF = (ll)mod17 * mod17;
typedef pair<int, int>P;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
using ld = double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void chmin(T& a, T b) {
a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
a = max(a, b);
}
template<typename T>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
vector<T> res;
int ida = 0, idb = 0;
while (ida < a.size() || idb < b.size()) {
if (idb == b.size()) {
res.push_back(a[ida]); ida++;
}
else if (ida == a.size()) {
res.push_back(b[idb]); idb++;
}
else {
if (a[ida] < b[idb]) {
res.push_back(a[ida]); ida++;
}
else {
res.push_back(b[idb]); idb++;
}
}
}
return res;
}
template<typename T>
void cinarray(vector<T>& v) {
rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
rep(i, v.size()) {
if (i > 0)cout << " "; cout << v[i];
}
cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
if (n < 0) {
ll res = mod_pow(x, -n, m);
return mod_pow(res, m - 2, m);
}
if (abs(x) >= m)x %= m;
if (x < 0)x += m;
//if (x == 0)return 0;
ll res = 1;
while (n) {
if (n & 1)res = res * x % m;
x = x * x % m; n >>= 1;
}
return res;
}
//mod should be <2^31
struct modint {
int n;
modint() :n(0) { ; }
modint(ll m) {
if (m < 0 || mod <= m) {
m %= mod; if (m < 0)m += mod;
}
n = m;
}
operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
if (n == 0)return modint(1);
modint res = (a * a) ^ (n / 2);
if (n % 2)res = res * a;
return res;
}
ll inv(ll a, ll p) {
return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
fact[0] = modint(1);
for (int i = 0; i < max_n - 1; i++) {
fact[i + 1] = fact[i] * modint(i + 1);
}
factinv[max_n - 1] = modint(1) / fact[max_n - 1];
for (int i = max_n - 2; i >= 0; i--) {
factinv[i] = factinv[i + 1] * modint(i + 1);
}
}
modint comb(int a, int b) {
if (a < 0 || b < 0 || a < b)return 0;
return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
if (a < 0 || b < 0 || a < b)return 0;
return fact[a] * factinv[a - b];
}
ll gcd(ll a, ll b) {
a = abs(a); b = abs(b);
if (a < b)swap(a, b);
while (b) {
ll r = a % b; a = b; b = r;
}
return a;
}
template<typename T>
void addv(vector<T>& v, int loc, T val) {
if (loc >= v.size())v.resize(loc + 1, 0);
v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
fill(isp + 2, isp + mn, true);
for (int i = 2; i < mn; i++) {
if (!isp[i])continue;
ps.push_back(i);
for (int j = 2 * i; j < mn; j += i) {
isp[j] = false;
}
}
}*/
//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
auto res = st.lower_bound(val);
if (res == st.begin())return st.end();
res--; return res;
}
//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
auto res = st.lower_bound(val);
return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
a = a + b; return a;
}
mP operator-(mP a, mP b) {
return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
a = a - b; return a;
}
LP operator+(LP a, LP b) {
return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
a = a + b; return a;
}
LP operator-(LP a, LP b) {
return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
a = a - b; return a;
}
mt19937 mt(time(0));
const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
//int dx[4] = { 1,0,-1,0 };
//int dy[4] = { 0,1,0,-1 };
//------------------------------------
template<typename T>
struct mcf {
private:
struct edge {
int to, cap; T cost; int rev; bool isrev; T oricost;
};
vector<vector<edge>> G;
vector<P> par;
vector<T> dist;
T inf = INF;
public:
mcf(int n) {
G.resize(n);
par.resize(n);
dist.resize(n);
}
void add_edge(int from, int to, int cap, T cost) {
G[from].push_back({ to,cap,cost,(int)G[to].size(),false,cost });
G[to].push_back({ from,0,-cost,(int)G[from].size() - 1,true,cost });
}
pair<T, int> minimum_road(int s, int t) {
fill(all(par), P{ -1,-1 });
fill(all(dist), inf);
dist[s] = 0;
priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>> q;
q.push({ 0,s });
while (!q.empty()) {
pair<T, int> p = q.top(); q.pop();
int id = p.second;
if (id == t)continue;
if (p.first > dist[id])continue;
rep(j, G[id].size()) {
if (G[id][j].cap > 0) {
int to = G[id][j].to;
T nd = p.first + G[id][j].cost;
if (nd < dist[to]) {
dist[to] = nd;
par[to] = { id,j };
q.push({ dist[to],to });
}
}
}
}
int cur = t;
int f = 1;
cur = t;
while (cur != s) {
int p = par[cur].first, j = par[cur].second;
if (p < 0)return { -1,-1 };
G[p][j].cap -= f;
int adc = 2;
if (G[p][j].rev >= 0) {
G[cur][G[p][j].rev].cap += f;
G[cur][G[p][j].rev].cost = -G[p][j].cost;
}
G[p][j].cost += 2 * G[p][j].oricost;
cur = p;
}
return { dist[t],f };
}
T minimum_cost_flow(int s, int t, int k) {
T ret = 0;
rep(i, k) {
pair<T, int> z = minimum_road(s, t);
if (z.first < 0)return -1;
if (k - i <= z.second) {
ret += z.first * (k - i); break;
}
i += z.second - 1;
ret += z.first * z.second;
}
return ret;
}
};
using T = ll;
using TP = pair<T, T>;
bool isg(TP a, TP b) {
return a.first * b.second < a.second* b.first;
}
void solve() {
int n, m; cin >> n >> m;
mcf<ll> mc(n);
rep(i, m) {
int a, b, c; cin >> a >> b >> c; a--; b--;
if (b == 0 || a == n - 1)continue;
mc.add_edge(a, b, mod17, c);
}
ll sum = 0;
TP res = { mod17,1 };
for (int c = 1;c<=100; c++) {
ll val= mc.minimum_cost_flow(0, n - 1, 1);
sum += val;
//cout << c << " " << sum << "\n";
TP nex = { sum,(ll)c * c };
if (isg(nex, res)) {
res = nex;
}
}
modint ans = res.first % mod;
modint ans2 = res.second % mod;
ans = ans / ans2;
cout << ans << "\n";
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
//cout << fixed<<setprecision(10);
//init_f();
//init();
//while(true)
//expr();
int t; cin >> t; rep(i, t)
solve();
return 0;
}
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