#include #include #define rep(i,b) for(int i=0;i=0;i--) #define rep1(i,b) for(int i=1;i=x;i--) #define fore(i,a) for(auto& i:a) #define rng(x) (x).begin(), (x).end() #define rrng(x) (x).rbegin(), (x).rend() #define sz(x) ((int)(x).size()) #define pb push_back #define fi first #define se second #define pcnt __builtin_popcountll using namespace std; using namespace atcoder; using ll = long long; using ld = long double; template using mpq = priority_queue, greater>; template bool chmax(T &a, const T &b) { if (a bool chmin(T &a, const T &b) { if (b ll sumv(const vector&a){ll res(0);for(auto&&x:a)res+=x;return res;} bool yn(bool a) { if(a) {cout << "Yes" << endl; return true;} else {cout << "No" << endl; return false;}} #define retval(x) {cout << #x << endl; return;} #define cout2(x,y) cout << x << " " << y << endl; #define coutp(p) cout << p.fi << " " << p.se << endl; #define out cout << ans << endl; #define outd cout << fixed << setprecision(20) << ans << endl; #define outm cout << ans.val() << endl; #define outv fore(yans , ans) cout << yans << "\n"; #define outdv fore(yans , ans) cout << yans.val() << "\n"; #define assertmle(x) if (!x) {vi v(3e8);} #define asserttle(x) if (!x) {while(1){}} #define coutv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;} #define coutv2(v) fore(vy , v) cout << vy << "\n"; #define coutvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;} #define coutvm2(v) fore(vy , v) cout << vy.val() << "\n"; using pll = pair;using pil = pair;using pli = pair;using pii = pair;using pdd = pair; using vi = vector;using vd = vector;using vl = vector;using vs = vector;using vb = vector; using vpii = vector;using vpli = vector;using vpll = vector;using vpil = vector; using vvi = vector>;using vvl = vector>;using vvs = vector>;using vvb = vector>; using vvpii = vector>;using vvpli = vector>;using vvpll = vector;using vvpil = vector; using mint = modint998244353; //using mint = modint1000000007; //using mint = dynamic_modint<0>; using vm = vector; using vvm = vector>; vector dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1}; ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;} ll lcm(ll a, ll b) { return a/gcd(a,b)*b;} #define yes {cout <<"Yes"< exp; matexp(int n) : n(n){ exp.resize(logmax,vvm(n,vm(n))); } vvm mat_product(vvm& a,vvm& b){ int n1 = sz(a); int m1 = sz(a[0]); int n2 = sz(b); int m2 = sz(b[0]); assert(m1 == n2); vvm ret(n1,vm(m2)); rep(i,n1) rep(j,m2) rep(k,m1) ret[i][j] += a[i][k]*b[k][j]; return ret; } void init(vvm a){ exp[0] = a; rep1(i,logmax) exp[i] = mat_product(exp[i-1],exp[i-1]); } vvm getexp_k(ll k){ vvm ret(n,vm(n)); rep(i,n) ret[i][i] = 1; rep(i,logmax) if ((k >> i & 1) == 1) ret = mat_product(ret,exp[i]); return ret; } }; // A^k (Aは行列)を計算 // matexp(n) : n(行列の次元)を初期化 // mat_product(a,b) : 行列積a*bを返す // init(a) : 行列Aを初期化 // getexp_k : A^kを返す void solve(){ ll n,m,k; cin>>n>>m>>k; ll p = m-1; auto f = [&](auto f, ll n, ll m, ll k)->mint{ if (m == 1){ mint ret = mint(p).pow(n); return ret; } if (n == 0){ return 1; } ll nn = n-1; ll d = gcd(m,k); ll nm = m/d; ll nk = k; mint coef = (p+1)/m-1; if (d == 1){ vvm a(3,vm(3)); a[0][0] = -1; a[0][2] = coef+1; a[1][0] = 1; a[2][2] = p; matexp me(3); me.init(a); vvm v = me.getexp_k(n); mint ret = v[1][0]*coef + v[1][1] + v[1][2]*p; return ret; } mint zero = f(f,nn,nm,nk); mint other = mint(p).pow(nn) - zero; mint ret = (coef+1)*other + coef*zero; return ret; }; mint ans = f(f,n,m,k); outm; return; } int main(){ ios::sync_with_stdio(false); cin.tie(0); int t = 1; //cin>>t; rep(i,t){ solve(); } return 0; }