/* #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") //*/ #include // #include using namespace std; // using namespace atcoder; #define DEBUG(x) cerr << #x << ": " << x << endl; #define DEBUG_VEC(v) \ cerr << #v << ":"; \ for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \ cerr << " " << v[iiiiiiii]; \ cerr << endl; #define DEBUG_MAT(v) \ cerr << #v << endl; \ for (int i = 0; i < v.size(); i++) { \ for (int j = 0; j < v[i].size(); j++) { \ cerr << v[i][j] << " "; \ } \ cerr << endl; \ } typedef long long ll; // #define int ll #define vi vector #define vl vector #define vii vector> #define vll vector> #define vs vector #define pii pair #define pis pair #define psi pair #define pll pair template pair operator+(const pair &s, const pair &t) { return pair(s.first + t.first, s.second + t.second); } template pair operator-(const pair &s, const pair &t) { return pair(s.first - t.first, s.second - t.second); } template ostream &operator<<(ostream &os, pair p) { os << "(" << p.first << ", " << p.second << ")"; return os; } #define X first #define Y second #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rrep1(i, n) for (int i = (int)(n); i > 0; i--) #define REP(i, a, b) for (int i = a; i < b; i++) #define in(x, a, b) (a <= x && x < b) #define all(c) c.begin(), c.end() void YES(bool t = true) { cout << (t ? "YES" : "NO") << endl; } void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; } void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; } void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; } void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; } void no(bool t = true) { cout << (t ? "no" : "yes") << endl; } template bool chmax(T &a, const T &b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T &a, const T &b) { if (a > b) { a = b; return 1; } return 0; } #define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end()); const ll inf = 1000000001; const ll INF = (ll)1e18 + 1; const long double pi = 3.1415926535897932384626433832795028841971L; int popcount(ll t) { return __builtin_popcountll(t); } // int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; // int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 }; vi dx = {0, 1, 0, -1}, dy = {-1, 0, 1, 0}; // vi dx2 = { 1,1,0,-1,-1,-1,0,1 }, dy2 = { 0,1,1,1,0,-1,-1,-1 }; struct Setup_io { Setup_io() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << fixed << setprecision(25); } } setup_io; // const ll MOD = 1000000007; const ll MOD = 998244353; // #define mp make_pair //#define endl '\n' signed main() { int n, k; cin >> n >> k; vector dp(n + 1, vll(k, vl(k))); rep(i, k) rep(j, k) { if (i == j) continue; dp[2][i][j]++; } vector dpl(n + 1, vll(k, vl(k))), dpu(n + 1, vll(k, vl(k))); ll ans = 0; for (int i = 2; i < n; i++) { rep(j, k) { rep(l, k) { if (j > 0) { dpl[i][j][l] = (dpl[i][j - 1][l] + dp[i][j - 1][l]) % MOD; } } } rrep(j, k) { rep(l, k) { if (j + 1 < k) { dpu[i][j][l] = (dpu[i][j + 1][l] + dp[i][j + 1][l]) % MOD; } } } rep(l, k) { rep(x, k) { if (x == l) continue; if (l > x) { (dp[i + 1][l][x] += dpl[i][l][l] - dp[i][x][l]) %= MOD; } else { (dp[i + 1][l][x] += dpu[i][l][l] - dp[i][x][l]) %= MOD; } } } } ll ans1 = 0; rep(j, k) rep(l, k) ans1 += dp[n][j][l]; ans1 %= MOD; cout << (ans1 + MOD) % MOD << " "; ll ans2 = 0; rep(i, n) { int l = i, r = n - 1 - i; for (int x = 0; x < k; x++) { // DEBUG(pii(i, x)); // ue { ll addl = 0, addr = 0; if (l == 0) { addl = 1; } else if (l == 1) { addl = k - 1 - x; } else { for (int u = x + 1; u < k; u++) { addl += (dpl[l][u][u] - dp[l][x][u]); } } addl %= MOD; if (r == 0) { addr = 1; } else if (r == 1) { addr = k - 1 - x; } else { for (int u = x + 1; u < k; u++) { addr += (dpl[r][u][u] - dp[r][x][u]); } } addr %= MOD; ll kumi = addl % MOD * addr % MOD; for (int u = x + 1; u < k; u++) { ll subl = 0, subr = 0; if (l == 0) subl = 0; else if (l == 1) subl = 1; else { subl = dpl[l][u][u] - dp[l][x][u]; } if (r == 0) subr = 0; else if (r == 1) subr = 1; else { subr = dpl[r][u][u] - dp[r][x][u]; } kumi -= subl % MOD * subr % MOD; } kumi %= MOD; // DEBUG(kumi); ans2 += kumi * x % MOD; } { // sita ll addl = 0, addr = 0; if (l == 0) { addl = 1; } else if (l == 1) { addl = x; } else { for (int u = x - 1; u >= 0; u--) { addl += (dpu[l][u][u] - dp[l][x][u]); } } addl %= MOD; if (r == 0) { addr = 1; } else if (r == 1) { addr = x; } else { for (int u = x - 1; u >= 0; u--) { addr += (dpu[r][u][u] - dp[r][x][u]); } } addr %= MOD; ll kumi = addl % MOD * addr % MOD; for (int u = x - 1; u >= 0; u--) { ll subl = 0, subr = 0; if (l == 0) subl = 0; else if (l == 1) subl = 1; else { subl = dpu[l][u][u] - dp[l][x][u]; } if (r == 0) subr = 0; else if (r == 1) subr = 1; else { subr = dpu[r][u][u] - dp[r][x][u]; } kumi -= subl % MOD * subr % MOD; } kumi %= MOD; // DEBUG(kumi); ans2 += kumi * x % MOD; } // DEBUG(ans2); } } ans2 = (ans2 % MOD + MOD) % MOD; cout << ans2 << endl; }