#include using namespace std; using ll = long long; /* p = 2^m a + 1 mod root 998244353 3 924844033 5 */ const ll modc = 998244353; const ll root = 3; class mint { ll x; public: mint(ll x=0) : x((x%modc+modc)%modc) {} mint operator-() const { return mint(-x); } mint& operator+=(const mint& a) { if ((x += a.x) >= modc) x -= modc; return *this; } mint& operator-=(const mint& a) { if ((x += modc-a.x) >= modc) x -= modc; return *this; } mint& operator*=(const mint& a) { (x *= a.x) %= modc; return *this; } mint operator+(const mint& a) const { mint res(*this); return res+=a; } mint operator-(const mint& a) const { mint res(*this); return res-=a; } mint operator*(const mint& a) const { mint res(*this); return res*=a; } mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } mint inv() const { return pow(modc-2); } mint& operator/=(const mint& a) { return (*this) *= a.inv(); } mint operator/(const mint& a) const { mint res(*this); return res/=a; } bool operator == (const mint& a) const{ return x == a.x; } friend ostream& operator<<(ostream& os, const mint& m){ os << m.x; return os; } friend istream& operator>>(istream& ip, mint &m) { ll t; ip >> t; m = mint(t); return ip; } ll val(){ return x; } }; vector ntt(vector a, bool inv = false){ ll N = a.size(), m = 0, q = (modc-1)/N; // N=2^m, p=2^m q+1 // g = r^q (DFT) // g = r^-q (IDFT) //p=2^m q+1 //r^(p-1) = 1 //r^(2^m q) = 1 //(r^q) ^ (2^m) = 1 //w_(2^m) = r^q //w_(2^(m-1)) = (r^q)^2 //w_(2^(m-2)) = (r^q)^4 for (int i=0; (1<>k & 1) << (m-1-k); if (i < j) swap(a[i], a[j]); } mint g = (inv ? mint(root).pow(q).inv() : mint(root).pow(q)); vector w(m+1); w[m] = g; for (int i=m-1; i>=1; i--) w[i] = w[i+1] * w[i+1]; for (int b=1, i=1; b convolution(vector a, vector b){ int s = a.size() + b.size() - 1; int t = 1; while(t < s) t *= 2; a.resize(t); b.resize(t); vector A = ntt(a); //DFT vector B = ntt(b); //DFT for (int i=0; i> N >> M >> X; mx = N*X; vector> a(5, vector(N)), b(5, vector(N)), c(5); for (int i=0; i> C; C--; a[C][i] = 1; } for (int i=0; i> A >> B >> C; A--; B--; b[B][N-1-A] += C; } for (int i=0; i<5; i++){ c[i] = convolution(a[i], b[i]); } for (int i=0; i