#include #include #define chmin(x,y) (x) = min((x),(y)) #define chmax(x,y) (x) = max((x),(y)) using namespace std; using namespace atcoder; using ll = long long; const ll mod = 998244353; using mint = modint998244353; using Graph = vector>; const vector dx = {1,0,-1,0}, dy = {0,1,0,-1}; int main(){ // input int N,M,K; cin >> N >> M >> K; // prep: list up all adequate adjacent pair of indices vector inv(M+1); for(int i = 1; i <= M; i++) inv[i] = M / i; vector can_l(M+1,-1),can_r(M+1,1); for(int i = 1; i <= M; i++) for(int j = 1; j <= M; j++) if(abs(inv[i]-inv[j]) <= K){ can_r[i] = j; if(can_l[i] == -1) can_r[i] = j; } // Check bounds on can_l and can_r to ensure they're within [1, M] for(int i = 1; i <= M; i++) { can_l[i] = max(1, can_l[i]); // Ensure can_l[i] is at least 1 can_r[i] = min(M, can_r[i]); // Ensure can_r[i] does not exceed M } // prep: doubling + ruisekiwa vector> dbl(31,vector(M+1,0)); vector>> rui(31,vector>(M+1,vector(M+1,0))); for(int i = 1; i <= M; i++) dbl[0][i] = 1; for(int i = 1; i <= M; i++) for(int j = 1; j <= M; j++) rui[0][i][j] = rui[0][i-1][j] + rui[0][i][j-1] - rui[0][i-1][j-1] + dbl[0][i]; for(int i = 0; i < 30; i++){ for(int j = 1; j <= M; j++){ vector tmp(M+1); for(int k = 1; k <= M; k++){ mint add = (rui[i][can_r[k]][j] - rui[i][can_l[k]-1][j] - rui[i][can_r[k]][j-1] + rui[i][can_l[k]-1][j-1]); dbl[i+1][j] += dbl[i][k] * add; tmp[k] = add; } for(int k = 1; k <= M; k++) rui[i+1][j][k] = rui[i][j-1][k] + rui[i][j][k-1] - rui[i][j-1][k-1] + tmp[k]; } } // solve: DP accelerated by doubling vector> dp(31,vector(M+1,0)); for(int j = 1; j <= M; j++) dp[0][j] = 1; --N; for(int i = 0; i < 30; i++){ for(int j = 1; j <= M; j++){ if(N & (1 << i)){ for(int k = 1; k <= M; k++){ mint add = (rui[i][can_r[k]][j] - rui[i][can_l[k]-1][j] - rui[i][can_r[k]][j-1] + rui[i][can_l[k]-1][j-1]); dp[i+1][j] += dp[i][k] * add; } } else dp[i+1][j] = dp[i][j]; } } // output mint ans = 0; for(int j = 1; j <= M; j++) ans += dp[30][j]; cout << ans.val() << endl; }