#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 <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")

////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
  static unsigned M;
  static unsigned long long NEG_INV_M;
  static void setM(unsigned long long m) { M = m; NEG_INV_M = -1ULL / M; }
  unsigned x;
  ModInt() : x(0U) {}
  ModInt(unsigned x_) : x(x_ % M) {}
  ModInt(unsigned long long x_) : x(x_ % M) {}
  ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) {
    const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
    const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
    const unsigned long long r = y - M * q;
    x = r - M * (r >= M);
    return *this;
  }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////

using Mint = ModInt;


// singular ==> return false;
// solution: a[j][n]
bool solveEq(vector<vector<Mint>> &a) {
  const int n = a.size();
  for (int h = 0; h < n; ++h) {
    for (int i = h; i < n; ++i) if (a[i][h]) {
      swap(a[h], a[i]);
      break;
    }
    if (!a[h][h]) return false;
    const Mint s = a[h][h].inv();
    for (int j = h + 1; j <= n; ++j) a[h][j] *= s;
    for (int i = h + 1; i < n; ++i) {
      for (int j = h + 1; j <= n; ++j) a[i][j] -= a[i][h] * a[h][j];
    }
  }
  for (int i = n; --i >= 0; ) {
    for (int j = i + 1; j < n; ++j) a[i][n] -= a[i][j] * a[j][n];
  }
  return true;
}


int N, MO, I;
vector<int> L;
vector<Mint> P, D;

int M;
vector<int> LL;


namespace sub3 {
Mint run() {
  vector<vector<int>> graph(M, vector<int>(N));
  for (int u = 0; u < M; ++u) {
    for (int i = 0; i < N; ++i) {
      graph[u][i] = (u / LL[i] % L[i] == L[i] - 1) ? (u - LL[i] * (L[i] - 1)) : (u + LL[i]);
    }
  }
  Mint ans = 1;
  for (int t = 1; t < M; ++t) {
    vector<vector<Mint>> a(M, vector<Mint>(M + 1, 0));
    a[t][M] = 1;
    for (int u = 0; u < M; ++u) {
      a[u][u] = 1;
      if (u != 0 && u != t) {
        for (int i = 0; i < N; ++i) {
          a[u][graph[u][i]] -= P[i];
        }
      }
    }
    const bool res = solveEq(a);
    assert(res);
    Mint sum = 0;
    for (int i = 0; i < N; ++i) {
      sum += P[i] * a[graph[0][i]][M];
    }
    ans += sum;
  }
  return ans;
}
}  // sub3


namespace sub4 {
#define N do_not_use_N
#define M do_not_use_M
Mint f[1025][32][33];
Mint run() {
  if (L[0] < L[1]) {
    swap(L[0], L[1]);
    swap(P[0], P[1]);
  }
  Mint ans = 1;
  for (int tx = 0; tx < L[0]; ++tx) for (int ty = 0; ty < L[1]; ++ty) if (tx || ty) {
    for (int x = 0; x <= L[0]; ++x) for (int y = 0; y < L[1]; ++y) {
      fill(f[x][y], f[x][y] + (L[1] + 1), 0);
    }
    for (int y = 0; y < L[1]; ++y) {
      f[L[0]][y][y] = 1;
    }
    for (int x = L[0]; --x >= 0; ) {
      if (x == 0 || x == tx) {
        const int y0 = (x == 0) ? 0 : ty;
        for (int y = y0; ; ) {
          if (x == 0 && y == 0) {
            f[x][y][L[1]] = 0;
          } else if (x == tx && y == ty) {
            f[x][y][L[1]] = 1;
          } else {
            const int yy = (y + 1) % L[1];
            for (int z = 0; z <= L[1]; ++z) {
              f[x][y][z] = P[0] * f[x + 1][y][z] + P[1] * f[x][yy][z];
            }
          }
          if (y == 0) y = L[1];
          if (--y == y0) break;
        }
      } else {
        {
          Mint prob = P[0] / (1 - P[1].pow(L[1]));
          for (int yy = 0; yy < L[1]; ++yy) {
            for (int z = 0; z <= L[1]; ++z) {
              f[x][0][z] += prob * f[x + 1][yy][z];
            }
            prob *= P[1];
          }
        }
        for (int y = L[1]; --y >= 1; ) {
          const int yy = (y + 1) % L[1];
          for (int z = 0; z <= L[1]; ++z) {
            f[x][y][z] = P[0] * f[x + 1][y][z] + P[1] * f[x][yy][z];
          }
        }
      }
    }
    vector<vector<Mint>> a(L[1], vector<Mint>(L[1] + 1, 0));
    for (int y = 0; y < L[1]; ++y) {
      a[y][y] += 1;
      for (int z = 0; z < L[1]; ++z) {
        a[y][z] -= f[0][y][z];
      }
      a[y][L[1]] += f[0][y][L[1]];
    }
    const bool res = solveEq(a);
    assert(res);
    auto calc = [&](int x, int y) -> Mint {
      Mint ret = 0;
      for (int z = 0; z < L[1]; ++z) {
        ret += f[x][y][z] * a[z][L[1]];
      }
      ret += f[x][y][L[1]];
      return ret;
    };
    Mint sum = 0;
    sum += P[0] * calc(1, 0);
    sum += P[1] * calc(0, 1);
    ans += sum;
  }
  return ans;
}
#undef N
#undef M
}  // sub4


int main() {
  for (; ~scanf("%d%d%d", &N, &MO, &I); ) {
    Mint::setM(MO);
    L.resize(N);
    P.resize(N);
    D.resize(N);
    for (int i = 0; i < N; ++i) {
      scanf("%d%u%u", &L[i], &P[i].x, &D[i].x);
    }
    
    {
      Mint sumP = 0;
      for (int i = 0; i < N; ++i) {
        sumP += P[i];
      }
      const Mint invSumP = sumP.inv();
      for (int i = 0; i < N; ++i) {
        P[i] *= invSumP;
      }
    }
    
    LL.resize(N + 1);
    LL[0] = 1;
    for (int i = 0; i < N; ++i) {
      LL[i + 1] = LL[i] * L[i];
    }
    M = LL[N];
cerr<<"N = "<<N<<", M = "<<M<<", I = "<<I<<", L = "<<L<<endl;
    
    Mint ans;
    if (I == 1) {
      ans = M;
    } else if (I == 2 || I == 3) {
      ans = sub3::run();
    } else if (I == 4) {
      ans = sub4::run();
    }
    printf("%u\n", ans.x);
  }
  return 0;
}