#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define mod1 1000000007 #define mod2 998244353 #define mod3 100000007 #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> // using mint = modint998244353; template void debug(T e) { cerr << e << endl; } template void debug(vector &v) { rep(i, v.size()) { cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v) { rep(i, v.size()) { rep(j, v[i].size()) { cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v) { rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st) { for (auto itr = st.begin(); itr != st.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms) { for (auto itr = ms.begin(); itr != ms.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(map &mp) { for (auto itr = mp.begin(); itr != mp.end(); itr++) { cerr << itr->first << " " << itr->second << endl; } } void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << H << " "; debug_out(T...); } using mint = modint998244353; void debug_mint1(vector &vec) { for (int i = 0; i < vec.size(); i++) { cerr << vec[i].val() << " "; } cerr << endl; } void debug_mint2(vector> &vec) { for (int i = 0; i < vec.size(); i++) { for (int j = 0; j < vec[i].size(); j++) { cerr << vec[i][j].val() << " "; } cerr << endl; } } int main() { ll N, K; cin >> N >> K; vector dp1(N, vector(K, vector(K, mint(0)))); vector dp2(N, vector(K, vector(K, mint(0)))); for (ll i = 0; i < K; i++) { for (ll j = 0; j < K; j++) { if (i == j) { continue; } dp1[1][i][j] = mint(1); dp2[1][i][j] = mint(i + j); } } for (ll i = 2; i < N; i++) { // 前の dp の累積和を求める vector> dpsum1(K + 1, vector(K, mint(0))); for (ll j = 1; j <= K; j++) { for (ll k = 0; k < K; k++) { dpsum1[j][k] += (dpsum1[j - 1][k] + dp1[i - 1][j - 1][k]); } } vector> dpsum2(K + 1, vector(K, mint(0))); for (ll j = 1; j <= K; j++) { for (ll k = 0; k < K; k++) { dpsum2[j][k] += (dpsum2[j - 1][k] + dp2[i - 1][j - 1][k]); } } // debug_mint2(dp1[i - 1]); // debug_mint2(dp2[i - 1]); for (ll j = 0; j < K; j++) { for (ll k = 0; k < K; k++) { if (j == k) { continue; } else if (j < k) { // dp1[j + 1][j] + dp1[j + 2][j] + ... + dp1[K - 1][j] dp1[i][j][k] += (dpsum1[K][j] - dpsum1[j + 1][j] - dp1[i - 1][k][j]); dp2[i][j][k] += (dpsum1[K][j] - dpsum1[j + 1][j] - dp1[i - 1][k][j]) * mint(k); dp2[i][j][k] += (dpsum2[K][j] - dpsum2[j + 1][j] - dp2[i - 1][k][j]); } else { // dp1[0][j] + dp1[1][j] + ... + dp1[j - 1][j] dp1[i][j][k] += (dpsum1[j][j] - dp1[i - 1][k][j]); dp2[i][j][k] += (dpsum1[j][j] - dp1[i - 1][k][j]) * mint(k); dp2[i][j][k] += (dpsum2[j][j] - dp2[i - 1][k][j]); } } } } // debug_mint2(dp1[N - 1]); // debug_mint2(dp2[N - 1]); mint ans1 = mint(0); mint ans2 = mint(0); for (ll i = 0; i < K; i++) { for (ll j = 0; j < K; j++) { ans1 += dp1[N - 1][i][j]; ans2 += dp2[N - 1][i][j]; } } cout << ans1.val() << " " << ans2.val() << endl; }