#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 {
using BigInt = vector<int>;
constexpr int BASE = 10;
BigInt toBigInt(Int a) {
  BigInt ret;
  do {
    ret.push_back(a % BASE);
    a /= BASE;
  } while (a);
  return ret;
}
BigInt toBigInt(const string &s) {
  BigInt ret;
  for (const char c : s) {
    ret.push_back(c - '0');
  }
  reverse(ret.begin(), ret.end());
  return ret;
}
BigInt add(const BigInt &a, const BigInt &b) {
  BigInt c(a.size() + b.size() + 1, 0);
  for (int i = 0; i < (int)a.size(); ++i) c[i] += a[i];
  for (int i = 0; i < (int)b.size(); ++i) c[i] += b[i];
  for (int i = 0; i < (int)c.size() - 1; ++i) {
    if (c[i] >= BASE) {
      c[i + 1] += 1;
      c[i] -= BASE;
    }
  }
  return c;
}
BigInt sub(const BigInt &a, const BigInt &b) {
  BigInt c(a.size() + b.size() + 1, 0);
  for (int i = 0; i < (int)a.size(); ++i) c[i] += a[i];
  for (int i = 0; i < (int)b.size(); ++i) c[i] -= b[i];
  for (int i = 0; i < (int)c.size() - 1; ++i) {
    if (c[i] < 0) {
      c[i + 1] -= 1;
      c[i] += BASE;
    }
  }
  return c;
}
BigInt mul(BigInt p, Int q) {
  Int r = 0;
  for (int i = 0; i < (int)p.size(); ++i) {
    r += p[i] * q;
    p[i] = r % BASE;
    r /= BASE;
  }
  for (; r; ) {
    p.push_back(r % BASE);
    r /= BASE;
  }
  return p;
}
pair<BigInt, int> divmod(BigInt p, int q) {
  long long r = 0;
  for (int i = (int)p.size(); --i >= 0; ) {
    r = r * BASE + p[i];
    p[i] = r / q;
    assert(p[i] < BASE);
    r %= q;
  }
  return make_pair(p, r);
}
int cmp(const BigInt &a, const BigInt &b) {
  for (int i = max((int)a.size(), (int)b.size()); --i >= 0; ) {
    const int aa = (i < (int)a.size()) ? a[i] : 0;
    const int bb = (i < (int)b.size()) ? b[i] : 0;
    if (aa < bb) return -1;
    if (aa > bb) return +1;
  }
  return 0;
}

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);
  }
  
  using Cyc = pair<pair<Int, int>, int>;
  vector<Cyc> 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 Cyc &cyc0, const Cyc &cyc1) -> bool {
    return (cyc0.first.first * cyc1.first.second < cyc1.first.first * cyc0.first.second);
  });
  const int cycsLen = cycs.size();
// cerr<<"cycs = "<<cycs<<endl;
  
  const BigInt K0 = toBigInt(K);
  vector<int> can(N, 0);
  vector<BigInt> mns(N);
  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> ids(N, -2);
    for (int j = 0; j < j0; ++j) {
      ids[cycs[j].second] = -1;
    }
    if (!~ids[0]) {
      continue;
    }
    int U = 0;
    for (int u = 0; u < N; ++u) if (~ids[u]) {
      ids[u] = U++;
    }
    vector<int> on(U, 0);
    for (int j = j0; j < j1; ++j) {
      on[ids[cycs[j].second]] = 1;
    }
// cerr<<"p = "<<p<<", q = "<<q<<", ids = "<<ids<<", on = "<<on<<endl;
    vector<int> as, bs;
    vector<Int> cs;
    for (int i = 0; i < M; ++i) if (~ids[A[i]] && ~ids[B[i]]) {
      as.push_back(ids[A[i]]);
      bs.push_back(ids[B[i]]);
      cs.push_back(C[i]);
    }
    const int m = as.size();
    const auto q0r0 = divmod(K0, q);
    const int r0 = q0r0.second;
    vector<Int> here(U, INF);
    vector<Int> crt(U << 1, INF);
    crt[0 << 1 | on[0]] = 0;
    for (int k = 0; k < U + q * U; ++k) {
      if (k % q == r0) {
        for (int x = 0; x < U; ++x) {
          const Int c = crt[x << 1 | 1];
          if (c < INF) {
            chmin(here[x], c + (N - k / q) * p);
          }
        }
      }
      vector<Int> nxt(U << 1, INF);
      for (int i = 0; i < m; ++i) {
        chmin(nxt[bs[i] << 1 | on[bs[i]]], crt[as[i] << 1 | 0] + cs[i]);
        chmin(nxt[bs[i] << 1 | 1], crt[as[i] << 1 | 1] + cs[i]);
      }
      crt.swap(nxt);
    }
    const BigInt c0 = mul(sub(q0r0.first, toBigInt(N)), p);
    for (int u = 0; u < N; ++u) {
      const int x = ids[u];
      if (~x && here[x] < INF) {
        assert(here[x] >= 0);
        const BigInt c = add(c0, toBigInt(here[x]));
        if (mns[u].empty() || cmp(mns[u], c) > 0) {
          mns[u] = c;
        }
      }
    }
  }
  vector<int> ans(N, -1);
  for (int u = 0; u < N; ++u) if (!mns[u].empty()) {
    ans[u] = divmod(mns[u], MO).second;
  }
  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;
}