#include <bits/stdc++.h>
using namespace std;
# if __cplusplus >= 201700LL
# define INLINE_V inline
# else
# define INLINV_V
# endif
#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0)
x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v)
v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1)
return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1)
r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1)
return false;
if (n == 2 || n == 7 || n == 61)
return true;
if (n % 2 == 0)
return false;
long long d = n - 1;
while (d % 2 == 0)
d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0)
return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0)
m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2)
return 1;
if (m == 167772161)
return 3;
if (m == 469762049)
return 3;
if (m == 754974721)
return 11;
if (m == 998244353)
return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0)
x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok)
return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_MATH_HPP
#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type,
std::false_type>::type;
template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using to_unsigned =
typename std::conditional<is_signed_int128<T>::value, make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type;
template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type;
#endif
template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_TYPE_TRAITS_HPP
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr> struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr> static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0)
x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); }
unsigned int val() const { return _v; }
mint &operator++() {
_v++;
if (_v == umod())
_v = 0;
return *this;
}
mint &operator--() {
if (_v == 0)
_v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod())
_v -= umod();
return *this;
}
mint &operator-=(const mint &rhs) {
_v -= rhs._v;
if (_v >= umod())
_v += umod();
return *this;
}
mint &operator*=(const mint &rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr> dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0)
x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); }
unsigned int val() const { return _v; }
mint &operator++() {
_v++;
if (_v == umod())
_v = 0;
return *this;
}
mint &operator--() {
if (_v == 0)
_v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod())
_v -= umod();
return *this;
}
mint &operator-=(const mint &rhs) {
_v += mod() - rhs._v;
if (_v >= umod())
_v -= umod();
return *this;
}
mint &operator*=(const mint &rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#endif // ATCODER_MODINT_HPP
#define ll long long
#define ull unsigned long long
#define rep(i, f, t, ...) for (int i = f, ##__VA_ARGS__; i <= t; ++i)
#define red(i, f, t, ...) for (int i = f, ##__VA_ARGS__; i >= t; --i)
#define emb emplace_back
#define pb push_back
#define pii pair<int, int>
#define mkp make_pair
#define arr3 array<int, 3>
#define arr4 array<int, 4>
#define FILEIO(filename) freopen(filename ".in", "r", stdin), freopen(filename ".out", "w", stdout)
#define ALrep(vc) vc.begin(), vc.end()
#define N 605
template <class T> constexpr static T inf = numeric_limits<T>::max() / 10;
#ifdef MACOS
#include "/Users/yzw/GeorgeYuOI/codes/cpp/georgeyucjr/debug/debug.hpp"
using namespace georgeyucjr;
#else
#define write(...) void(36)
#define bug(...) void(36)
#endif
bool Mst;
using mint = atcoder::modint998244353;
using i128 = __int128_t;
using db = long double;
INLINE_V constexpr static i128 VAL1 = 2e18;
INLINE_V constexpr static i128 VAL2 = 1e31;
INLINE_V constexpr static i128 VAL3 = 1e27;
int n, m, Eu[N], Ev[N];
ll k, Ew[N];
namespace Solve1 { // k <= 2 * n * n
i128 dis[N], updis[N];
inline void span() {
fill(updis + 1, updis + n + 1, 2 * inf<i128>);
rep(i, 1, m) updis[Ev[i]] = min(updis[Ev[i]], dis[Eu[i]] + Ew[i]);
copy_n(updis + 1, n, dis + 1);
}
i128 cyc[N][N], ray[N][N];
inline void SLVR() {
fill(dis + 1, dis + n + 1, 2 * inf<i128>);
dis[1] = 0;
ll LEN = n * (n + 1) * 3;
if (k <= 2 * LEN)
rep(t, 1, k) span();
else {
ll mid = k - LEN * 2;
rep(i, 1, n) {
fill(dis + 1, dis + n + 1, 2 * inf<i128>);
dis[i] = 0;
rep(j, 1, n) span(), cyc[i][j] = ((dis[i] < inf<i128>) ? (dis[i]) : (-1));
}
fill(dis + 1, dis + n + 1, 2 * inf<i128>);
dis[1] = 0;
rep(t, 1, LEN) span();
rep(i, 1, n) rep(j, 1, n) ray[i][j] = 2 * inf<i128>;
rep(i, 1, n) if (dis[i] < inf<i128>) rep(j, 1, n) if (~cyc[i][j]) {
ll t = mid / j + 1;
ll sm = t * j - mid;
ray[sm][i] = min(ray[sm][i], dis[i] + (i128)t * cyc[i][j]);
}
fill(dis + 1, dis + n + 1, 2 * inf<i128>);
rep(t, 1, LEN) {
span();
if (t <= n)
rep(i, 1, n) dis[i] = min(dis[i], ray[t][i]);
}
}
rep(i, 1, n) cout << ( dis[i] > inf < i128 > ? -1 : ( int ) mint ( dis[i] ).val ( ) ) << ( i == n ? "\n" : " ");
}
} // namespace Solve1
namespace Solve2 { // k > 2 * n * n
i128 dis[N], updis[N];
struct Frac {
int L;
i128 S;
Frac(i128 sum = 0, int len = 0) { L = len, S = sum; }
};
inline bool operator<(const Frac &lhs, const Frac &rhs) { return lhs.S * rhs.L < rhs.S * lhs.L; }
inline bool operator==(const Frac &lhs, const Frac &rhs) { return lhs.S * rhs.L == rhs.S * lhs.L; }
struct Node {
Frac a, b;
Node(Frac A = Frac(1, 1), Frac B = Frac(1, 1)) { a = A, b = B; }
};
bool flag;
i128 K, LIM;
inline bool operator<(const Node &x, const Node &y) {
i128 vl1 = x.a.S * y.a.L;
i128 vl2 = x.a.L * y.a.S;
if (vl1 == vl2)
return x.b < y.b;
if (flag)
return vl1 < vl2;
i128 dt = vl1 - vl2;
return (-LIM <= dt && dt <= LIM) ? dt * K + x.b.S * y.b.L < x.b.L * y.b.S : vl1 < vl2;
}
INLINE_V const static Node Nd_inf = Node(Frac(VAL2, 1), Frac(VAL2, 1));
inline void span() {
fill(updis + 1, updis + n + 1, 2 * inf<i128>);
rep(i, 1, m) updis[Ev[i]] = min(updis[Ev[i]], dis[Eu[i]] + Ew[i]);
copy_n (updis + 1, n, dis + 1);
}
Node tempdis[N], tempud[N];
inline void SAP() {
fill(tempud + 1, tempud + n + 1, Nd_inf);
rep(i, 1, m) {
auto cur = tempdis[Eu[i]];
cur.b.S += (__int128)Ew[i] * cur.b.L;
tempud[Ev[i]] = min(tempud[Ev[i]], cur);
}
copy_n(tempud + 1, n, tempdis + 1);
}
i128 cyc[N][N];
Node ray[N][N];
inline void SLVR(string S) {
fill(dis + 1, dis + n + 1, 2 * inf<i128>);
dis[1] = 0;
ll LEN = n * (n + 1) * 2;
db tmp = 0;
for (auto ch : S)
tmp = tmp * 10 + (ch ^ 48);
if (tmp > VAL3) {
flag = true;
} else {
flag = false;
K = 0;
for (auto ch : S)
K = K * 10 + (ch ^ 48);
K -= LEN * 2;
if (K)
LIM = 2e36 / K;
}
rep(i, 1, n) {
fill(dis + 1, dis + n + 1, 2 * inf<i128>);
dis[i] = 0;
rep(j, 1, n) span(), cyc[i][j] = ((dis[i] < inf<i128>) ? dis[i] : -1);
}
fill(dis + 1, dis + n + 1, 2 * inf<i128>);
dis[1] = 0;
rep(t, 1, LEN) span();
vector<int> mds(n + 1);
rep(i, 1, n, w) {
w = 0;
for (; auto &ch : S)
w = w * 10 + (ch ^ 48), w %= i;
mds[i] = ((w - LEN * 2) % i + i) % i;
}
rep(i, 1, n) rep(j, 1, n) ray[i][j] = Nd_inf;
rep(i, 1, n) if (dis[i] < inf<i128>) rep(j, 1, n, md, sm) if (~cyc[i][j])
sm = j - (md = mds[j]),
ray[sm][i] = min(ray[sm][i], Node(Frac(cyc[i][j], j), Frac(dis[i] * j + sm * cyc[i][j], j)));
rep(i, 1, n) tempdis[i] = Nd_inf;
rep(t, 1, LEN) {
SAP();
if (t <= n)
rep(i, 1, n) tempdis[i] = min(tempdis[i], ray[t][i]);
}
mint num = 0;
for (auto ch : S)
(num *= 10) += (ch ^ 48);
num -= LEN * 2;
rep(i, 1, n) {
auto r = tempdis[i];
if ((db)r.a.S / r.a.L > VAL1)
cout << -1 << " ";
else
cout << ((num * r.a.S + r.b.S) * mint(r.b.L).inv()).val() << " ";
}
cout << endl;
}
} // namespace Solve2
bool Med;
signed main() {
#ifndef ONLINE_JUDGE
freopen("ex_matrix2.in", "r", stdin), freopen("P10000.out", "w", stdout);
// FILEIO("P10000");
#endif
ios_base ::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
auto slv = [&]() {
string S;
cin >> n >> m >> S;
db tmp = 0;
for (auto ch : S)
tmp = tmp * 10 + (ch ^ 48);
rep(i, 1, m) cin >> Eu[i] >> Ev[i] >> Ew[i];
if (tmp <= n * n * 10) {
k = 0;
for (auto ch : S)
k = k * 10 + (ch ^ 48);
Solve1::SLVR();
return;
}
Solve2::SLVR(S);
};
int T;
cin >> T >> T;
while (T--)
slv();
#ifdef MACOS
cerr << "Memory & Time Information : " << endl;
cerr << "Memory : " << ((&Med) - (&Mst)) * 1. / 1024. / 1024. << "MB" << endl;
cerr << "Time : " << clock() * 1. / CLOCKS_PER_SEC * 1000. << "ms" << endl;
#endif
return 0;
}