#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

// using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


#ifndef LIBRA_OTHER_INT128_H_
#define LIBRA_OTHER_INT128_H_

#include <stdio.h>
#include <iostream>

constexpr unsigned __int128 toUInt128(const char *s) {
  unsigned __int128 x = 0;
  for (; *s; ++s) x = x * 10 + (*s - '0');
  return x;
}
constexpr __int128 toInt128(const char *s) {
  if (*s == '-') return -toInt128(s + 1);
  __int128 x = 0;
  for (; *s; ++s) x = x * 10 + (*s - '0');
  return x;
}
unsigned __int128 inUInt128() {
  static char buf[41];
  scanf("%s", buf);
  return toUInt128(buf);
}
__int128 inInt128() {
  static char buf[41];
  scanf("%s", buf);
  return toInt128(buf);
}

void out(unsigned __int128 x) {
  static char buf[41];
  int len = 0;
  do { buf[len++] = '0' + static_cast<int>(x % 10); } while (x /= 10);
  for (int i = len; --i >= 0; ) putchar(buf[i]);
}
void out(__int128 x) {
  if (x < 0) {
    putchar('-');
    out(-static_cast<unsigned __int128>(x));
  } else {
    out(static_cast<unsigned __int128>(x));
  }
}
std::ostream &operator<<(std::ostream &os, unsigned __int128 x) {
  static char buf[41];
  int len = 0;
  do { buf[len++] = '0' + static_cast<int>(x % 10); } while (x /= 10);
  for (int i = len; --i >= 0; ) os << buf[i];
  return os;
}
std::ostream &operator<<(std::ostream &os, __int128 x) {
  if (x < 0) {
    os << '-' << -static_cast<unsigned __int128>(x);
  } else {
    os << static_cast<unsigned __int128>(x);
  }
  return os;
}

#endif  // LIBRA_OTHER_INT128_H_


using Int = __int128;
constexpr Int INF = toInt128("1002003004005006007006005004003002001");

constexpr unsigned MO = 998244353;

char buf[110];

int S;
int N, M;
string K;
vector<int> A, B;
vector<Int> C;


namespace small {
vector<int> run() {
cerr<<"[small::run]"<<endl;
  const int K0 = stoi(K);
  vector<Int> crt(N, INF);
  crt[0] = 0;
  for (int k = 0; k < K0; ++k) {
    vector<Int> nxt(N, INF);
    for (int i = 0; i < M; ++i) {
      chmin(nxt[B[i]], crt[A[i]] + C[i]);
    }
    crt.swap(nxt);
  }
  vector<int> ans(N, -1);
  for (int u = 0; u < N; ++u) if (crt[u] < INF) {
    ans[u] = crt[u] % MO;
  }
  return ans;
}
}  // small


namespace large {
vector<int> run() {
cerr<<"[large::run]"<<endl;
  vector<vector<int>> G(N);
  for (int i = 0; i < M; ++i) {
    G[A[i]].push_back(i);
  }
  
  vector<pair<pair<Int, int>, int>> cycs;
  for (int s = 0; s < N; ++s) {
    Int pm = 1;
    int qm = 0;
    vector<Int> crt(N, INF);
    crt[s] = 0;
    for (int k = 1; k <= N; ++k) {
      vector<Int> nxt(N, INF);
      for (int i = 0; i < M; ++i) {
        chmin(nxt[B[i]], crt[A[i]] + C[i]);
      }
      crt.swap(nxt);
      Int p = crt[s];
      int q = k;
      if (p < INF) {
        if (pm * q > p * qm) {
          pm = p;
          qm = q;
        }
      }
    }
    if (qm) {
      cycs.emplace_back(make_pair(pm, qm), s);
    }
  }
  sort(cycs.begin(), cycs.end());
  const int cycsLen = cycs.size();
// cerr<<"cycs = "<<cycs<<endl;
  
  // TODO
  const Int K0 = toInt128(K.c_str());
  vector<Int> mns(N, INF);
  for (int j0 = 0, j1 = 0; j0 < cycsLen; j0 = j1) {
    for (; j1 < cycsLen && cycs[j0].first == cycs[j1].first; ++j1) {}
    const Int p = cycs[j0].first.first;
    const int q = cycs[j0].first.second;
    vector<int> on(N, 0);
    for (int j = j0; j < j1; ++j) {
      on[cycs[j].second] = 1;
    }
    const Int c0 = (K0 / q) * p;
    const int r0 = K0 % q;
    vector<Int> here(N, INF);
    vector<Int> crt(N << 1, INF);
    crt[0 << 1 | on[0]] = 0;
    for (int k = 0; k < N + q * N; ++k) {
      if (k % q == r0) {
        for (int u = 0; u < N; ++u) if (crt[u << 1 | 1] < INF) {
          chmin(here[u], crt[u << 1 | 1] - (k / q) * p);
        }
      }
      vector<Int> nxt(N << 1, INF);
      for (int i = 0; i < M; ++i) {
        chmin(nxt[B[i] << 1 | on[B[i]]], crt[A[i] << 1 | 0] + C[i]);
        chmin(nxt[B[i] << 1 | 1], crt[A[i] << 1 | 1] + C[i]);
      }
      crt.swap(nxt);
    }
    for (int u = 0; u < N; ++u) if (here[u] < INF) {
      chmin(mns[u], c0 + here[u]);
    }
  }
  vector<int> ans(N, -1);
  for (int u = 0; u < N; ++u) if (mns[u] < INF) {
    ans[u] = mns[u] % MO;
  }
  return ans;
}
}  // large


int main() {
  for (int numCases; ~scanf("%d%d", &S, &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    scanf("%d%d%s", &N, &M, buf);
    K = buf;
    A.resize(M);
    B.resize(M);
    C.resize(M);
    for (int i = 0; i < M; ++i) {
      scanf("%d%d", &A[i], &B[i]);
      --A[i];
      --B[i];
      C[i] = inInt128();
    }
    
    vector<int> ans;
    if (K.size() <= 9 && stoi(K) <= N * N) {
      ans = small::run();
    } else {
      ans = large::run();
    }
    
    for (int u = 0; u < N; ++u) {
      if (u) printf(" ");
      printf("%d", ans[u]);
    }
#ifdef LOCAL
printf(" ");
#endif
    puts("");
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}