import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintStream; import java.io.PrintWriter; import java.lang.annotation.ElementType; import java.lang.annotation.Retention; import java.lang.annotation.RetentionPolicy; import java.lang.annotation.Target; import java.lang.reflect.Array; import java.math.BigInteger; import java.nio.file.Files; import java.nio.file.OpenOption; import java.nio.file.Path; import java.nio.file.Paths; import java.util.ArrayDeque; import java.util.ArrayList; import java.util.Arrays; import java.util.Collection; import java.util.Collections; import java.util.Comparator; import java.util.Deque; import java.util.HashMap; import java.util.HashSet; import java.util.List; import java.util.Map.Entry; import java.util.Map; import java.util.NoSuchElementException; import java.util.Optional; import java.util.Queue; import java.util.Random; import java.util.Set; import java.util.TreeMap; import java.util.TreeSet; import java.util.function.BiFunction; import java.util.function.Consumer; import java.util.function.DoubleUnaryOperator; import java.util.function.IntBinaryOperator; import java.util.function.IntFunction; import java.util.function.IntToDoubleFunction; import java.util.function.IntToLongFunction; import java.util.function.IntUnaryOperator; import java.util.function.LongBinaryOperator; import java.util.function.LongToDoubleFunction; import java.util.function.Predicate; import java.util.function.Supplier; import java.util.function.ToIntFunction; import java.util.random.RandomGenerator; import java.util.stream.IntStream; import java.util.stream.Stream; class FastScanner { private static FastScanner instance = null; private final InputStream in = System.in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int buflen = 0; private FastScanner() { } public static FastScanner getInstance() { if (instance == null) { instance = new FastScanner(); } return instance; } private boolean hasNextByte() { if (ptr < buflen) { return true; } ptr = 0; try { buflen = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } return buflen > 0; } private int readByte() { if (hasNextByte()) { return buffer[ptr++]; } else { return -1; } } private boolean isPrintableChar(int c) { return (33 <= c) && (c <= 126); } public boolean hasNext() { while (hasNextByte() && (!isPrintableChar(buffer[ptr]))) { ptr++; } return hasNextByte(); } public long nextLong() { if (!hasNext()) { throw new NoSuchElementException(); } long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } while ((b >= '0') && (b <= '9')) { // n = n * 10 + (b - '0'); n = ((n << 1) + (n << 3)) + (b - '0'); b = readByte(); } return minus ? -n : n; } public int nextInt() { return ((int) (nextLong())); } public int[] nextInts(int n) { int[] a = new int[n]; for (int i = 0; i < n; ++i) { a[i] = nextInt(); } return a; } } class MergeFiles {} class PolynomialFp { public static final long mod = 998244353;// 119×2^{23}+1 static long[][] bitreversedRoots = new long[30][]; static long[][] bitreversedInvRoots = new long[30][]; static long ADD(long a, long b) { long sum = a + b; return sum >= mod ? sum - mod : sum; } static long SUB(long a, long b) { return ADD(a, mod - b); } static void prepareRoots(int n) { int sz = Integer.numberOfTrailingZeros(n); if (bitreversedRoots[sz] != null) { return; } long g = 3; long root = MathUtils.modPow(g, (mod - 1) / n, mod); long iroot = MathUtils.modInv(root, mod); bitreversedRoots[sz] = new long[n]; bitreversedInvRoots[sz] = new long[n]; for (int n_ = n / 2; n_ >= 1; n_ /= 2 , root = (root * root) % mod , iroot = (iroot * iroot) % mod) { long w = 1; long iw = 1; for (int j = 0; j < n_; ++j) { bitreversedRoots[sz][n_ + j] = w; bitreversedInvRoots[sz][n_ + j] = iw; w = (w * root) % mod; iw = (iw * iroot) % mod; } int cur = 0; for (int j = 0; j < n_; ++j) { if (cur < j) { ArrayUtils.swap(n_ + cur, n_ + j, bitreversedRoots[sz]); ArrayUtils.swap(n_ + cur, n_ + j, bitreversedInvRoots[sz]); } for (int k = n_ / 2; k > (cur ^= k); k /= 2); } } } /** * fftをbitreversedした順で返す。 * Scott, Michael. "A note on the implementation of the number theoretic transform." IMA International Conference on Cryptography and Coding. Cham: Springer International Publishing, 2017. * * @param a */ public static void fftTobitReversed(long[] a) { int n = a.length; int sz = Integer.numberOfTrailingZeros(a.length); if (bitreversedRoots[sz] == null) { prepareRoots(a.length); } for (int m = 1, t = n / 2; m <= (n / 2); m *= 2 , t /= 2) { for (int i = 0, k = 0; i < m; ++i , k += 2 * t) { long S = bitreversedRoots[sz][m + i]; for (int j = k; j < (k + t); ++j) { long u = a[j]; long v = (a[j + t] * S) % mod; a[j] = ADD(u, v); a[j + t] = SUB(u, v); } } } } /** * Scott, Michael. "A note on the implementation of the number theoretic transform." IMA International Conference on Cryptography and Coding. Cham: Springer International Publishing, 2017. * * @param a */ public static void ifftFromBitreversed(long[] a) { long invN = MathUtils.modInv(a.length, mod); int n = a.length; int sz = Integer.numberOfTrailingZeros(n); if (bitreversedInvRoots[sz] == null) { prepareRoots(a.length); } for (int m = n / 2, t = 1; m >= 1; m /= 2 , t *= 2) { for (int i = 0, k = 0; i < m; ++i , k += 2 * t) { long S = bitreversedInvRoots[sz][m + i]; if (m == 1) { S = (S * invN) % mod; } for (int j = k; j < (k + t); ++j) { long u = a[j]; long v = a[j + t]; if (m == 1) { a[j] = ((u + v) * invN) % mod; } else { a[j] = ADD(u, v); } a[j + t] = (((u + mod) - v) * S) % mod; } } } } static long[] mulFFT(long[] a, long[] b) { int n = 1; int len = (a.length + b.length) - 1; while (n < ((a.length + b.length) - 1)) { n *= 2; } a = Arrays.copyOf(a, n); b = Arrays.copyOf(b, n); prepareRoots(n); fftTobitReversed(a); fftTobitReversed(b); for (int i = 0; i < a.length; ++i) { a[i] = (a[i] * b[i]) % mod; } ifftFromBitreversed(a); return resize(a, len); } public static long[] mulNaive(long[] a, long[] b) { long[] ret = new long[(a.length + b.length) - 1]; for (int i = 0; i < a.length; ++i) { for (int j = 0; j < b.length; ++j) { ret[i + j] += a[i] * b[j]; ret[i + j] %= mod; } } return ret; } /** * [-mod+1, mod-1]の範囲外の要素があると、ADD/SUBでバグる。 * * @param a * @param b * @return */ public static long[] mul(long[] a, long[] b) { for (int i = 0; i < a.length; i++) { if (a[i] < 0) { a[i] += mod; } } for (int i = 0; i < b.length; i++) { if (b[i] < 0) { b[i] += mod; } } if ((((a.length + b.length) - 1) <= 512) || (Math.min(a.length, b.length) <= 10)) { return mulNaive(a, b); } else { return mulFFT(a, b); } } static long[] resize(long[] a, int len) { return Arrays.copyOf(a, len); } } class RelaxedConvolution { private int n; private final int m; private final long[] f; private final long[] g; private final long[] h; RelaxedConvolution(int m) { this.m = m; this.f = new long[m]; this.g = new long[m]; this.h = new long[m]; } static final long mod = 998244353; private void calc(int l1, int r1, int l2, int r2) { long[] c = PolynomialFp.mul(Arrays.copyOfRange(f, l1, r1), Arrays.copyOfRange(g, l2, r2)); for (int i = 0; (i < c.length) && (((i + l1) + l2) < m); i++) { h[(i + l1) + l2] = (h[(i + l1) + l2] + c[i]) % mod; } } public long add(long a, long b) { f[n] = a; g[n] = b; n++; int x = (n + 1) & (-(n + 1)); int s = 0; if (x <= n) { for (int i = 1; i <= x; i <<= 1) { calc(n - i, n, s, s + i); calc(s, s + i, n - i, n); s += i; } } else { int i = 1; for (; i < (x / 2); i <<= 1) { calc(n - i, n, s, s + i); calc(s, s + i, n - i, n); s += i; } calc(n - i, n, s, s + i); } return h[n - 1]; } } class ArrayUtils { public static void swap(int i, int j, long[] A) { if (i == j) { return; } long tmp = A[i]; A[i] = A[j]; A[j] = tmp; } public static void swap(long[] A, long[] B) { if (A.length != B.length) { throw new AssertionError(); } for (int i = 0; i < A.length; i++) { long tmp = A[i]; A[i] = B[i]; B[i] = tmp; } } } class MyPrintWriter extends PrintWriter { private static MyPrintWriter instance = null; private MyPrintWriter() { super(System.out); } public static MyPrintWriter getInstance() { if (instance == null) { instance = new MyPrintWriter(); } return instance; } public void println(boolean[][] a) { for (int i = 0; i < a.length; i++) { println(a[i], " "); } } public void println(boolean[] a, String separator) { for (int i = 0; i < a.length; ++i) { super.print((a[i] ? 1 : 0) + (i == (a.length - 1) ? "\n" : separator)); } } } class Fp { final long mod; long[] fac = new long[0]; long[] ifac = new long[0]; long[] inv = new long[0]; public Fp(long mod) { this.mod = mod; } public void expand(int n) { fac = new long[n]; ifac = new long[n]; inv = new long[n]; Arrays.fill(fac, 1); Arrays.fill(ifac, 1); Arrays.fill(inv, 1); for (int i = 2; i < n; ++i) { fac[i] = (i * fac[i - 1]) % mod; inv[i] = mod - (((mod / i) * inv[((int) (mod % i))]) % mod); ifac[i] = (inv[i] * ifac[i - 1]) % mod; } } public long fac(int n) { if (fac.length <= n) { expand(Math.max(2 * fac.length, n + 1)); } return fac[n]; } public long inv(long n) { if (n < 0) { n = reduce(n); } return n < inv.length ? inv[((int) (n))] : MathUtils.modInv(n, mod); } /** * * * 剰余を取り、0以上mod未満の値を返す。 * * @param a * @return */ public long reduce(long a) { a %= mod; if (a < 0) { a += mod; } return a; } } class MathUtils { public static long modPow(long a, long n, long mod) { if (n < 0) { long inv = MathUtils.modInv(a, mod); return MathUtils.modPow(inv, -n, mod); } if (n == 0) { return 1; } return (MathUtils.modPow((a * a) % mod, n / 2, mod) * ((n % 2) == 1 ? a : 1)) % mod; } /** * 拡張ユークリッドの互除法で逆元を求める。 * * @param a * @param mod * @return */ public static long modInv(long a, long mod) { a = ((a % mod) + mod) % mod; long[] f0 = new long[]{ 1, 0, mod }; long[] f1 = new long[]{ 0, 1, a }; while (f1[2] != 0) { long q = f0[2] / f1[2]; for (int i = 0; i < 3; i++) { f0[i] -= q * f1[i]; } ArrayUtils.swap(f0, f1); } return f0[1] < 0 ? mod + f0[1] : f0[1]; } } public class Main implements Runnable { public static void main(String[] args) throws IOException { Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1)); // Runtime runtime = Runtime.getRuntime(); // new Thread(null, new Main(), "MainThreadWithLargeStack", (1024 * 1024) * 1024).start(); // new Main().test(); // new Main().gen(); new Main().run(); // long usedMemory = runtime.totalMemory() - runtime.freeMemory(); // System.err.printf("使用メモリ: %.2f MB%n", usedMemory / 1024.0 / 1024.0); MyPrintWriter.getInstance().flush(); } @Override public void run() { Random rnd = new Random(); FastScanner sc = FastScanner.getInstance(); MyPrintWriter pw = MyPrintWriter.getInstance(); long mod = 998244353; Fp fp = new Fp(mod); int N = sc.nextInt(); int M = sc.nextInt(); int[] A = sc.nextInts(M); Arrays.sort(A); long[] dp2 = new long[N + 1]; dp2[0] = 1; boolean[] contains = new boolean[N + 1]; for (int a : A) { contains[a] = true; } // for (int i = 0; i < A.length; i++) { // for (int j = 0; j < A[i]; j++) { // dp2[A[i]]+=dp2[j]*fp.fac(A[i]-Math.max(j-1, 0))%mod*2%mod*(mod-1)%mod; // dp2[A[i]]%=mod; // } // } long[] dp = new long[N + 1]; dp[0] = 1; RelaxedConvolution cnv = new RelaxedConvolution(N + 10); cnv.add(0, fp.reduce((-2) * 2)); for (int i = 1; i < contains.length; i++) { long v = cnv.add(i == 1 ? 0 : dp[i - 1], fp.reduce((-2) * fp.fac(i + 2))); if (!contains[i]) { continue; } // j = 0 の // dp[i] += dp[0] * fp.fac(i)(-2) // を別処理 v += (fp.fac(i) % mod) * (-2); v = fp.reduce(v); dp[i] = v; } long all = fp.fac(N); long alt = 0; for (int i = 0; i < dp.length; i++) { alt += (dp[i] * fp.fac(N - Math.max(i - 1, 0))) % mod; alt %= mod; } long even = (((alt + all) % mod) * fp.inv(2)) % mod; pw.println(even); } } // --- Original Code --- // package template; // // import java.io.IOException; // import java.util.Arrays; // import java.util.Random; // // import lib.tools.FastScanner; // import lib.tools.MergeFiles; // import lib.tools.MyPrintWriter; // import lib.util.Fp; // import lib.util.polynomial.PolynomialFp; // // public class Main implements Runnable { // // public static void main(String[] args) throws IOException { // // Runtime runtime = Runtime.getRuntime(); // // new Thread(null, new Main(), "MainThreadWithLargeStack", (1024 * 1024) * 1024).start(); // // new Main().test(); // // new Main().gen(); // new Main().run(); // // long usedMemory = runtime.totalMemory() - runtime.freeMemory(); // // System.err.printf("使用メモリ: %.2f MB%n", usedMemory / 1024.0 / 1024.0); // MyPrintWriter.getInstance().flush(); // MergeFiles.export(); // } // // @Override // public void run() { // Random rnd = new Random(); // FastScanner sc = FastScanner.getInstance(); // MyPrintWriter pw = MyPrintWriter.getInstance(); // long mod=998244353; // Fp fp=new Fp(mod); // int N=sc.nextInt(); // int M=sc.nextInt(); // int[]A=sc.nextInts(M); // Arrays.sort(A); // long[]dp2=new long[N+1]; // dp2[0]=1; // boolean[]contains=new boolean[N+1]; // for (int a : A) contains[a] = true; // // for (int i = 0; i < A.length; i++) { // // for (int j = 0; j < A[i]; j++) { // // dp2[A[i]]+=dp2[j]*fp.fac(A[i]-Math.max(j-1, 0))%mod*2%mod*(mod-1)%mod; // // dp2[A[i]]%=mod; // // } // // } // // long[]dp=new long[N+1]; // dp[0]=1; // RelaxedConvolution cnv=new RelaxedConvolution(N+10); // cnv.add(0, fp.reduce(-2*2)); // for (int i = 1; i < contains.length; i++) { // long v=cnv.add(i==1?0:dp[i - 1], fp.reduce(-2*fp.fac(i+2))); // if (!contains[i]) continue; // // j = 0 の // // dp[i] += dp[0] * fp.fac(i)(-2) // // を別処理 // v += fp.fac(i) % mod * (-2); // v = fp.reduce(v); // dp[i] = v; // } // long all=fp.fac(N); // long alt=0; // for (int i = 0; i < dp.length; i++) { // alt+=dp[i]*fp.fac(N-Math.max(i-1, 0))%mod; // alt%=mod; // } // long even=(alt+all)%mod*fp.inv(2)%mod; // pw.println(even); // // } // // // // // // // void gen() { // Random rnd = new Random(); // MyPrintWriter pw = MyPrintWriter.getInstance(); // } // // void test() { // Random rnd = new Random(); // for (int TEST = 0; TEST < 10000; TEST++) { // } // } // // void abc() { // Random rnd = new Random(); // int a = rnd.nextInt(212, 445); // System.out.println(a); // } // // void tr(Object... objects) { // System.out.println(Arrays.deepToString(objects)); // } // // // // // } // // // // class RelaxedConvolution { // private int n; // // private final int m; // // private final long[] f; // // private final long[] g; // // private final long[] h; // // RelaxedConvolution(int m) { // this.m = m; // this.f = new long[m]; // this.g = new long[m]; // this.h = new long[m]; // } // // static final long mod = 998244353; // // private void calc(int l1, int r1, int l2, int r2) { // long[] c = PolynomialFp.mul(Arrays.copyOfRange(f, l1, r1), Arrays.copyOfRange(g, l2, r2)); // for (int i = 0; (i < c.length) && (((i + l1) + l2) < m); i++) { // h[(i + l1) + l2] = (h[(i + l1) + l2] + c[i]) % mod; // } // } // // public long add(long a, long b) { // f[n] = a; // g[n] = b; // n++; // int x = (n + 1) & (-(n + 1)); // int s = 0; // if (x <= n) { // for (int i = 1; i <= x; i <<= 1) { // calc(n - i, n, s, s + i); // calc(s, s + i, n - i, n); // s += i; // } // } else { // int i = 1; // for (; i < (x / 2); i <<= 1) { // calc(n - i, n, s, s + i); // calc(s, s + i, n - i, n); // s += i; // } // calc(n - i, n, s, s + i); // } // return h[n - 1]; // } // } //