#include #include using namespace std; using namespace atcoder; //using mint = modint1000000007; //const int mod = 1000000007; using mint = modint998244353; const int mod = 998244353; //const int INF = 1e9; //const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i,l,r)for(int i=(l);i<(r);++i) #define rrep(i, n) for (int i = (n-1); i >= 0; --i) #define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i) #define all(x) (x).begin(),(x).end() #define allR(x) (x).rbegin(),(x).rend() #define endl "\n" #define P pair template inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; } // combination mod prime // https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619 struct combination { vector fact, ifact; combination(int n) :fact(n + 1), ifact(n + 1) { assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i; } mint operator()(int n, int k) { return com(n, k); } mint com(int n, int k) { //負の二項係数を考慮する場合にコメントアウトを外す //if (n < 0) return com(-n, k) * (k % 2 ? -1 : 1); if (k < 0 || k > n) return 0; return fact[n] * ifact[k] * ifact[n - k]; } mint inv(int n, int k) { //if (n < 0) return inv(-n, k) * (k % 2 ? -1 : 1); if (k < 0 || k > n) return 0; return ifact[n] * fact[k] * fact[n - k]; } mint p(int n, int k) { return fact[n] * ifact[n - k]; } }c(200005); int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int n, m; cin >> n >> m; int maxmex = min(n, m + 1); //dp[i][j]:=長さがjで[0,i)で構成されたmexがiの数列の数 vector> dp(maxmex + 1, vector(n + 1)); dp[0][0] = 1; rep(i, maxmex) { vectorx = dp[i]; rep(j, x.size())x[j] *= c.ifact[j]; vectory(n + 1); rep2(j, 1, y.size())y[j] = c.ifact[j]; auto z = convolution(x, y); rep(j, n + 1)dp[i + 1][j] = z[j] * c.fact[j]; } /*rep(i, maxmex + 1) { rep(j, n + 1) cout << dp[i][j].val() << " "; cout << endl; }*/ //dp2[i][j]:=長さがjでmexがiの数列の数 vector> dp2(maxmex + 1, vector(n + 1)); rep(i, maxmex + 1) { vectorx(n + 1); rep(j, n + 1)x[j] = c.ifact[j] * pow_mod(max(0, m - i), j, mod); vectory = dp[i]; rep(j, y.size())y[j] *= c.ifact[j]; auto z = convolution(x, y); rep(j, n + 1)dp2[i][j] = z[j] * c.fact[j]; /*cout << endl; rep(j, x.size()) cout << x[j].val() << " "; cout << endl; rep(j, y.size()) cout << y[j].val() << " "; cout << endl; rep(j, z.size()) cout << z[j].val() << " "; cout << endl;*/ } /*rep(i, maxmex + 1) { rep(j, n + 1) cout << dp2[i][j].val() << " "; cout << endl; }*/ mint ans = 0; /*rep2(i, 1, n + 1) {//数列の長さ rep(j, maxmex + 1) {//mex rep(k, i + 1) {//以下の数。 if ((m - j < 0) && (i - k > 0))continue; ans += c(n, i) * pow_mod(m + 1, n - i, mod)*j * dp[j][k] * c(i, k)*pow_mod(m - j, i - k, mod); } } }*/ rep2(i, 1, n + 1) { rep(j, maxmex + 1)ans += c(n, i) * pow_mod(m + 1, n - i, mod) * dp2[j][i] * j; } cout << ans.val() << endl; return 0; }