package contest211120; import java.io.*; import java.util.ArrayDeque; import java.util.Arrays; import java.util.InputMismatchException; import java.util.Queue; import java.util.function.IntUnaryOperator; import java.util.function.LongUnaryOperator; public class D2 { InputStream is; FastWriter out; String INPUT = ""; public void solve() { int m = ni(), n = ni(); long ans = pow(n, 2*m+1, mod); int[][] fif = enumFIF(500000, mod); for(int k = 1;k <= n && k-1 <= m;k++){ ans -= C(n,k,mod,fif) * pow(k, k-2, mod) % mod * pow(2, k-1, mod) % mod * fif[0][k-1] % mod * C(m,k-1,mod,fif) % mod * pow((long)(n-k)*(n-k)%mod, m-(k-1), mod) % mod; } ans %= mod; if(ans < 0)ans += mod; out.println(ans); } public static long C(int n, int r, int mod, int[][] fif) { if (n < 0 || r < 0 || r > n) return 0; return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod; } public static int[][] enumFIF(int n, int mod) { int[] f = new int[n + 1]; int[] invf = new int[n + 1]; f[0] = 1; for (int i = 1; i <= n; i++) { f[i] = (int) ((long) f[i - 1] * i % mod); } long a = f[n]; long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } invf[n] = (int) (p < 0 ? p + mod : p); for (int i = n - 1; i >= 0; i--) { invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod); } return new int[][]{f, invf}; } public static final int mod = 998244353; public static final int G = 3; // only 998244353 public static long[] mul(long[] a, long[] b) { return Arrays.copyOf(NTTStockham998244353.convolve(a, b), a.length+b.length-1); } public static long[] mul(long[] a, long[] b, int lim) { return Arrays.copyOf(NTTStockham998244353.convolve(a, b), lim); } // public static final int mod = 1000000007; // public static long[] mul(long[] a, long[] b) // { // if(Math.max(a.length, b.length) >= 3000){ // return Arrays.copyOf(NTTCRT.convolute(a, b, 3, mod), a.length+b.length-1); // }else{ // return mulnaive(a, b); // } // } // public static long[] mul(long[] a, long[] b, int lim) // { // if(Math.max(a.length, b.length) >= 3000){ // return Arrays.copyOf(NTTCRT.convolute(a, b, 3, mod), lim); // }else{ // return mulnaive(a, b, lim); // } // } public static final long big = (Long.MAX_VALUE/mod/mod-1)*mod*mod; public static long[] mulnaive(long[] a, long[] b) { long[] c = new long[a.length+b.length-1]; for(int i = 0;i < a.length;i++){ for(int j = 0;j < b.length;j++){ c[i+j] += a[i]*b[j]; if(c[i+j] >= big)c[i+j] -= big; } } for(int i = 0;i < c.length;i++)c[i] %= mod; return c; } public static long[] mulnaive(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length;i++){ for(int j = 0;j < b.length && i+j < lim;j++){ c[i+j] += a[i]*b[j]; if(c[i+j] >= big)c[i+j] -= big; } } for(int i = 0;i < c.length;i++)c[i] %= mod; return c; } public static long[] mul_(long[] a, long k) { for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod; return a; } public static long[] mul(long[] a, long k) { a = Arrays.copyOf(a, a.length); for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod; return a; } public static long[] add(long[] a, long[] b) { long[] c = new long[Math.max(a.length, b.length)]; for(int i = 0;i < a.length;i++)c[i] += a[i]; for(int i = 0;i < b.length;i++)c[i] += b[i]; for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod; return c; } public static long[] add(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i]; for(int i = 0;i < b.length && i < lim;i++)c[i] += b[i]; for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod; return c; } public static long[] sub(long[] a, long[] b) { long[] c = new long[Math.max(a.length, b.length)]; for(int i = 0;i < a.length;i++)c[i] += a[i]; for(int i = 0;i < b.length;i++)c[i] -= b[i]; for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod; return c; } public static long[] sub(long[] a, long[] b, int lim) { long[] c = new long[lim]; for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i]; for(int i = 0;i < b.length && i < lim;i++)c[i] -= b[i]; for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod; return c; } // F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x) // if want p-destructive, comment out flipping p just before returning. public static long[] inv(long[] p) { int n = p.length; long[] f = {invl(p[0], mod)}; for(int i = 0;i < p.length;i++){ if(p[i] == 0)continue; p[i] = mod-p[i]; } for(int i = 1;i < 2*n;i*=2){ long[] f2 = mul(f, f, Math.min(n, 2*i)); long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2*i)); for(int j = 0;j < f.length;j++){ f2p[j] += 2L*f[j]; if(f2p[j] >= mod)f2p[j] -= mod; if(f2p[j] >= mod)f2p[j] -= mod; } f = f2p; } for(int i = 0;i < p.length;i++){ if(p[i] == 0)continue; p[i] = mod-p[i]; } return f; } // differentiate public static long[] d(long[] p) { long[] q = new long[p.length]; for(int i = 0;i < p.length-1;i++){ q[i] = p[i+1] * (i+1) % mod; } return q; } // integrate public static long[] i(long[] p) { long[] q = new long[p.length]; for(int i = 0;i < p.length-1;i++){ q[i+1] = p[i] * invl(i+1, mod) % mod; } return q; } static long[] exp(long[] a) { return exp(a, a.length); } /** * https://cs.uwaterloo.ca/~eschost/publications/BoSc09-final.pdf * @verified https://judge.yosupo.jp/problem/exp_of_formal_power_series * @param a * @param lim * @return */ static long[] exp(long[] a, int lim) { long[] F = {1L}; long[] G = {1L}; long[] da = d(a); for(int m = 1;;m *= 2) { long[] G2 = mul(G, G, m); G = sub(mul_(G, 2), mul(F, G2, m)); long[] Q = Arrays.copyOf(da, m-1); long[] W = add(Q, mul(G, sub(d(F), mul(F, Q, m), m-1))); F = mul(F, add(new long[] {1}, sub(Arrays.copyOf(a, m), i(W))), m); if(m >= lim)break; } return Arrays.copyOf(F, lim); } // \int f'(x)/f(x) dx public static long[] ln(long[] f) { return i(mul(d(f), inv(f))); } // ln F(x) - k ln P(x) = 0 public static long[] pow(long[] p, long K) { int n = p.length; int tz = trailingZeros(p); if((long)tz*K >= n)return new long[n]; long[] pa = Arrays.copyOfRange(p, tz, n); int m = pa.length; // pa[0] must be 1 long base = pa[0]; long scale = invl(base, mod); for(int i = 0;i < m;i++)pa[i] = pa[i] * scale % mod; long[] lnp = Arrays.copyOf(ln(pa), m); for(int i = 0;i < m;i++)lnp[i] = lnp[i] * K % mod; long[] reta = exp(lnp); long kscale = pow(base, K, mod); for(int i = 0;i < m;i++)reta[i] = reta[i] * kscale % mod; long[] ret = new long[n]; System.arraycopy(reta, 0, ret, (int)(tz*K), (int)(n-tz*K)); return ret; } public static int trailingZeros(long[] a) { int ret = 0; for(long v : a) { if(v == 0) { ret++; }else { break; } } return ret; } /** * n=500000, K=10^9でpowより1.76倍遅い * @param a * @param K * @return */ public static long[] powNaive(long[] a, int K) { int n = a.length; long[] ret = {1}; for(int d = 31-Integer.numberOfLeadingZeros(K);d >= 0;d--) { ret = mul(ret, ret, n); if(K<<~d<0) { ret = mul(ret, a, n); } } return ret; } public static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } public static long[] reverse(long[] p) { long[] ret = new long[p.length]; for(int i = 0;i < p.length;i++){ ret[i] = p[p.length-1-i]; } return ret; } public static long[] reverse(long[] p, int lim) { long[] ret = new long[lim]; for(int i = 0;i < lim && i < p.length;i++){ ret[i] = p[p.length-1-i]; } return ret; } // [quotient, remainder] // remainder can be empty. // // deg(f)=n, deg(g)=m, f=gq+r, f=gq+r. // f* = x^n*f(1/x), // t=g*^-1 mod x^(n-m+1), q=(tf* mod x^(n-m+1))* public static long[][] div(long[] f, long[] g) { int n = f.length, m = g.length; if(n < m)return new long[][]{new long[0], Arrays.copyOf(f, n)}; long[] rf = reverse(f, n-m+1); long[] rg = reverse(g, n-m+1); long[] rq = mul(rf, inv(rg), n-m+1); long[] q = reverse(rq, n-m+1); long[] r = sub(f, mul(q, g, m-1), m-1); return new long[][]{q, r}; } ///////////////////// 基本操作ここまで ///////////////////// transform // destructive public static long[] divf(long[] a, int[][] fif) { for(int i = 0;i < a.length;i++)a[i] = a[i] * fif[1][i] % mod; return a; } // destructive public static long[] mulf(long[] a, int[][] fif) { for(int i = 0;i < a.length;i++)a[i] = a[i] * fif[0][i] % mod; return a; } public static long[] doExponentialTransform(long[] a, int[][] fif) { return mulf(exp(divf(Arrays.copyOf(a, a.length), fif)), fif); } public static long[] doLogarithmicTransform(long[] a, int[][] fif) { return mulf(Arrays.copyOf(ln(divf(Arrays.copyOf(a, a.length), fif)), a.length), fif); } public static class NTTStockham998244353 { private static final int P = 998244353, mod = P, G = 3; private static long[] wps; public static long[] convolve(long[] a, long[] b) { int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2); wps = new long[m]; long unit = pow(G, (P-1)/m); wps[0] = 1; for(int p = 1;p < m;p++) { wps[p] = wps[p-1] * unit % mod; } long[] fa = go(a, m, false); long[] fb = a == b ? fa : go(b, m, false); for(int i = 0;i < m;i++){ fa[i] = fa[i]*fb[i] % mod; } fa = go(fa, m, true); for(int i = 1, j = m-1;i < j;i++,j--) { long d = fa[i]; fa[i] = fa[j]; fa[j] = d; } return fa; } private static void fft(long[] X, long[] Y) { int s = 1; boolean eo = false; for(int n = X.length;n >= 4;n /= 2) { int m = n/2; for(int p = 0;p < m;p++) { long wp = wps[s*p]; long wk = (wp<<32)/P; for(int q = 0;q < s;q++) { long a = X[q + s*(p+0)]; long b = X[q + s*(p+m)]; long ndsts = a + b; if(ndsts >= 2*P)ndsts -= 2*P; long T = a - b + 2*P; long Q = wk*T>>>32; Y[q + s*(2*p+0)] = ndsts; Y[q + s*(2*p+1)] = wp*T-Q*P&(1L<<32)-1; } } s *= 2; eo = !eo; long[] D = X; X = Y; Y = D; } long[] z = eo ? Y : X; for(int q = 0;q < s;q++) { long a = X[q + 0]; long b = X[q + s]; z[q+0] = (a+b) % P; z[q+s] = (a-b+2*P) % P; } } // private static void fft(long[] X, long[] Y) // { // int s = 1; // boolean eo = false; // for(int n = X.length;n >= 4;n /= 2) { // int m = n/2; // for(int p = 0;p < m;p++) { // long wp = wps[s*p]; // for(int q = 0;q < s;q++) { // long a = X[q + s*(p+0)]; // long b = X[q + s*(p+m)]; // Y[q + s*(2*p+0)] = (a+b) % P; // Y[q + s*(2*p+1)] = (a-b+P) * wp % P; // } // } // s *= 2; // eo = !eo; // long[] D = X; X = Y; Y = D; // } // long[] z = eo ? Y : X; // for(int q = 0;q < s;q++) { // long a = X[q + 0]; // long b = X[q + s]; // z[q+0] = (a+b) % P; // z[q+s] = (a-b+P) % P; // } // } private static long[] go(long[] src, int n, boolean inverse) { long[] dst = Arrays.copyOf(src, n); fft(dst, new long[n]); if(inverse){ long in = invl(n); for(int i = 0;i < n;i++){ dst[i] = dst[i] * in % mod; } } return dst; } private static long pow(long a, long n) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret*ret % mod; if (n<<~x<0)ret = ret*a%mod; } return ret; } private static long invl(long a) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } } public static void main(String[] args) { new D2().run(); } public void run() { long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new FastWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-S+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } private boolean eof() { if(lenbuf == -1)return true; int lptr = ptrbuf; while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false; try { is.mark(1000); while(true){ int b = is.read(); if(b == -1){ is.reset(); return true; }else if(!isSpaceChar(b)){ is.reset(); return false; } } } catch (IOException e) { return true; } } private final byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } // private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } public static class FastWriter { private static final int BUF_SIZE = 1<<13; private final byte[] buf = new byte[BUF_SIZE]; private final OutputStream out; private int ptr = 0; private FastWriter(){out = null;} public FastWriter(OutputStream os) { this.out = os; } public FastWriter(String path) { try { this.out = new FileOutputStream(path); } catch (FileNotFoundException e) { throw new RuntimeException("FastWriter"); } } public FastWriter write(byte b) { buf[ptr++] = b; if(ptr == BUF_SIZE)innerflush(); return this; } public FastWriter write(char c) { return write((byte)c); } public FastWriter write(char[] s) { for(char c : s){ buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); } return this; } public FastWriter write(String s) { s.chars().forEach(c -> { buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); }); return this; } private static int countDigits(int l) { if (l >= 1000000000) return 10; if (l >= 100000000) return 9; if (l >= 10000000) return 8; if (l >= 1000000) return 7; if (l >= 100000) return 6; if (l >= 10000) return 5; if (l >= 1000) return 4; if (l >= 100) return 3; if (l >= 10) return 2; return 1; } public FastWriter write(int x) { if(x == Integer.MIN_VALUE){ return write((long)x); } if(ptr + 12 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } private static int countDigits(long l) { if (l >= 1000000000000000000L) return 19; if (l >= 100000000000000000L) return 18; if (l >= 10000000000000000L) return 17; if (l >= 1000000000000000L) return 16; if (l >= 100000000000000L) return 15; if (l >= 10000000000000L) return 14; if (l >= 1000000000000L) return 13; if (l >= 100000000000L) return 12; if (l >= 10000000000L) return 11; if (l >= 1000000000L) return 10; if (l >= 100000000L) return 9; if (l >= 10000000L) return 8; if (l >= 1000000L) return 7; if (l >= 100000L) return 6; if (l >= 10000L) return 5; if (l >= 1000L) return 4; if (l >= 100L) return 3; if (l >= 10L) return 2; return 1; } public FastWriter write(long x) { if(x == Long.MIN_VALUE){ return write("" + x); } if(ptr + 21 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } public FastWriter write(double x, int precision) { if(x < 0){ write('-'); x = -x; } x += Math.pow(10, -precision)/2; // if(x < 0){ x = 0; } write((long)x).write("."); x -= (long)x; for(int i = 0;i < precision;i++){ x *= 10; write((char)('0'+(int)x)); x -= (int)x; } return this; } public FastWriter writeln(char c){ return write(c).writeln(); } public FastWriter writeln(int x){ return write(x).writeln(); } public FastWriter writeln(long x){ return write(x).writeln(); } public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); } public FastWriter write(int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(IntUnaryOperator f, int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(f.applyAsInt(x)); } return this; } public FastWriter write(LongUnaryOperator f, long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(f.applyAsLong(x)); } return this; } public FastWriter writeln() { return write((byte)'\n'); } public FastWriter writeln(int... xs) { return write(xs).writeln(); } public FastWriter writeln(long... xs) { return write(xs).writeln(); } public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); } public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); } public FastWriter writeln(char[] line) { return write(line).writeln(); } public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; } public FastWriter writeln(String s) { return write(s).writeln(); } private void innerflush() { try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException e) { throw new RuntimeException("innerflush"); } } public void flush() { innerflush(); try { out.flush(); } catch (IOException e) { throw new RuntimeException("flush"); } } public FastWriter print(byte b) { return write(b); } public FastWriter print(char c) { return write(c); } public FastWriter print(char[] s) { return write(s); } public FastWriter print(String s) { return write(s); } public FastWriter print(int x) { return write(x); } public FastWriter print(long x) { return write(x); } public FastWriter print(double x, int precision) { return write(x, precision); } public FastWriter println(char c){ return writeln(c); } public FastWriter println(int x){ return writeln(x); } public FastWriter println(long x){ return writeln(x); } public FastWriter println(double x, int precision){ return writeln(x, precision); } public FastWriter print(int... xs) { return write(xs); } public FastWriter print(long... xs) { return write(xs); } public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); } public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); } public FastWriter println(int... xs) { return writeln(xs); } public FastWriter println(long... xs) { return writeln(xs); } public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); } public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); } public FastWriter println(char[] line) { return writeln(line); } public FastWriter println(char[]... map) { return writeln(map); } public FastWriter println(String s) { return writeln(s); } public FastWriter println() { return writeln(); } } public static void trnz(int... o) { for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" "); System.out.println(); } // print ids which are 1 public static void trt(long... o) { Queue stands = new ArrayDeque<>(); for(int i = 0;i < o.length;i++){ for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x)); } System.out.println(stands); } public static void tf(boolean... r) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } public static void tf(boolean[]... b) { for(boolean[] r : b) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } System.out.println(); } public void tf(long[]... b) { if(INPUT.length() != 0) { for (long[] r : b) { for (long x : r) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } System.out.println(); } } public void tf(long... b) { if(INPUT.length() != 0) { for (long x : b) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } } private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }