#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(t, 1, n) span(), cyc[i][t] = ((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() {
  rep(i, 1, n) tempud[i] = 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) {
  dis[0] = 1;
  fill(dis + 2, dis + n + 1, 2 * inf<i128>);
  ll LEN = n * (n + 1) * 2;

  db tmp = 0;
  for (auto ch : S)
    tmp = tmp * 10 + (ch ^ 48);
  if (tmp > VAL3) {
    flag = 1;
  } else {
    flag = 0;
    K = 0;
    for (auto c : S)
      K = K * 10 + c ^ 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(t, 1, n) span(), cyc[i][t] = 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) {
    int w = 0;
    for (auto &r : S)
      w = w * 10 + r ^ 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;
}