#819693 (Java21) No.2130 分配方法の数え上げ mod 998244353

• 問題: No.2130 分配方法の数え上げ mod 998244353
• ユーザー: Yu_212
• 提出日時: 2022-11-25 22:19:12
• 言語: Java21 (openjdk 21)
• 結果: AC
• 実行時間: 426 ms / 2,000 ms
• コード長: 13,904 bytes
• コンパイル時間: 3,718 ms
• コンパイル使用メモリ: 102,756 KB
• 実行使用メモリ: 81,832 KB
• 最終ジャッジ日時: 2024-10-02 04:54:26
• 合計ジャッジ時間: 9,820 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	56 ms; 37,344 KB
testcase_01	AC	55 ms; 37,396 KB
testcase_02	AC	55 ms; 37,544 KB
testcase_03	AC	57 ms; 37,448 KB
testcase_04	AC	55 ms; 37,532 KB
testcase_05	AC	57 ms; 37,248 KB
testcase_06	AC	54 ms; 37,164 KB
testcase_07	AC	56 ms; 37,540 KB
testcase_08	AC	57 ms; 37,376 KB
testcase_09	AC	55 ms; 37,304 KB
testcase_10	AC	157 ms; 52,168 KB
testcase_11	AC	156 ms; 52,376 KB
testcase_12	AC	56 ms; 37,408 KB
testcase_13	AC	157 ms; 52,164 KB
testcase_14	AC	158 ms; 52,332 KB
testcase_15	AC	54 ms; 37,172 KB
testcase_16	AC	156 ms; 52,156 KB
testcase_17	AC	212 ms; 59,852 KB
testcase_18	AC	349 ms; 70,992 KB
testcase_19	AC	342 ms; 71,100 KB
testcase_20	AC	151 ms; 52,368 KB
testcase_21	AC	349 ms; 71,052 KB
testcase_22	AC	60 ms; 37,604 KB
testcase_23	AC	354 ms; 70,812 KB
testcase_24	AC	157 ms; 52,268 KB
testcase_25	AC	341 ms; 70,868 KB
testcase_26	AC	151 ms; 52,156 KB
testcase_27	AC	421 ms; 81,728 KB
testcase_28	AC	57 ms; 37,176 KB
testcase_29	AC	426 ms; 81,832 KB
testcase_30	AC	55 ms; 37,392 KB
testcase_31	AC	55 ms; 37,384 KB
testcase_32	AC	54 ms; 37,664 KB
testcase_33	AC	56 ms; 37,452 KB
testcase_34	AC	54 ms; 37,640 KB
testcase_35	AC	56 ms; 37,076 KB
testcase_36	AC	56 ms; 37,556 KB
testcase_37	AC	54 ms; 37,468 KB

ソースコード

import java.io.*;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import java.util.stream.Collectors;

public class Main {
    static In in = new FastIn();
    static Out out = new Out(false);
    static final long inf = 0x1fffffffffffffffL;
    static final int iinf = 0x3fffffff;
    static final double eps = 1e-9;
    static long mod = 998244353;

    void solve() {
        long n = in.nextLong();
        int m = in.nextInt();
        if (n < m) {
            out.println(0);
            return;
        }
        long ans = Combination.pow(2, n);
        long a = 1;
        long b = 1;
        for (int i = 0; i < m; i++) {
            ans = (ans + mod - a * Combination.inv(b) % mod) % mod;
            b *= i + 1;
            a *= (n - i) % mod;
            a %= mod;
            b %= mod;
        }
        out.println(ans);
    }

    static class Combination {
        private static final int MEMO_THRESHOLD = 1000000;
        static long mod = Main.mod;
        private static final List<Long> inv = new ArrayList<>();
        private static final List<Long> fact = new ArrayList<>();
        private static final List<Long> invFact = new ArrayList<>();
        private static final Map<Long, List<Long>> pow = new HashMap<>();

        private static void buildInvTable(int n) {
            if (inv.isEmpty()) {
                inv.add(null);
                inv.add(1L);
            }
            for (int i = inv.size(); i <= n; i++) {
                inv.add(mod - inv.get((int)(mod % i)) * (mod / i) % mod);
            }
        }

        private static void buildFactTable(int n) {
            if (fact.isEmpty()) {
                fact.add(1L);
                invFact.add(1L);
            }
            for (int i = fact.size(); i <= n; i++) {
                fact.add(fact.get(i - 1) * i % mod);
                invFact.add(inv(fact.get(i)));
            }
        }

        public static void setupPowTable(long a) {
            pow.put(a, new ArrayList<>(Collections.singleton(1L)));
        }

        private static void rangeCheck(long n, long r) {
            if (n < r) {
                throw new IllegalArgumentException("n < r");
            }
            if (n < 0) {
                throw new IllegalArgumentException("n < 0");
            }
            if (r < 0) {
                throw new IllegalArgumentException("r < 0");
            }
        }

        static long fact(int n) {
            buildFactTable(n);
            return fact.get(n);
        }

        static long invFact(int n) {
            buildFactTable(n);
            return invFact.get(n);
        }

        private static long comb0(int n, int r) {
            rangeCheck(n, r);
            return fact(n) * invFact(r) % mod * invFact(n - r) % mod;
        }

        static long comb(long n, long r) {
            rangeCheck(n, r);
            if (n < MEMO_THRESHOLD) {
                return comb0((int)n, (int)r);
            }
            r = Math.min(r, n - r);
            long x = 1, y = 1;
            for (long i = 1; i <= r; i++) {
                x = x * (n - r + i) % mod;
                y = y * i % mod;
            }
            return x * inv(y) % mod;
        }

        private static long perm0(int n, int r) {
            rangeCheck(n, r);
            return fact(n) * invFact(n - r) % mod;
        }

        static long perm(long n, long r) {
            rangeCheck(n, r);
            if (n < MEMO_THRESHOLD) {
                return perm0((int)n, (int)r);
            }
            long x = 1;
            for (long i = 1; i <= r; i++) {
                x = x * (n - r + i) % mod;
            }
            return x;
        }

        static long homo(long n, long r) {
            return r == 0 ? 1 : comb(n + r - 1, r);
        }

        private static long inv0(int a) {
            buildInvTable(a);
            return inv.get(a);
        }

        static long inv(long a) {
            if (a < MEMO_THRESHOLD) {
                return inv0((int)a);
            }
            long b = mod;
            long u = 1, v = 0;
            while (b >= 1) {
                long t = a / b;
                a -= t * b;
                u -= t * v;
                if (a < 1) {
                    return (v %= mod) < 0 ? v + mod : v;
                }
                t = b / a;
                b -= t * a;
                v -= t * u;
            }
            return (u %= mod) < 0 ? u + mod : u;
        }

        static long pow(long a, long b) {
            if (pow.containsKey(a) && b < MEMO_THRESHOLD) {
                return powMemo(a, (int)b);
            }
            long x = 1;
            while (b > 0) {
                if (b % 2 == 1) {
                    x = x * a % mod;
                }
                a = a * a % mod;
                b >>= 1;
            }
            return x;
        }

        static long powMemo(long a, int b) {
            List<Long> powMemo = pow.get(a);
            while (powMemo.size() <= b) {
                powMemo.add(powMemo.get(powMemo.size() - 1) * a % Main.mod);
            }
            return powMemo.get(b);
        }
    }

    public static void main(String... args) {
        new Main().solve();
        out.flush();
    }
}

class FastIn extends In {
    private final BufferedInputStream reader = new BufferedInputStream(System.in);
    private final byte[] buffer = new byte[0x10000];
    private int i = 0;
    private int length = 0;

    public int read() {
        if (i == length) {
            i = 0;
            try {
                length = reader.read(buffer);
            } catch (IOException ignored) {
            }
            if (length == -1) {
                return 0;
            }
        }
        if (length <= i) {
            throw new RuntimeException();
        }
        return buffer[i++];
    }

    String next() {
        StringBuilder builder = new StringBuilder();
        int b = read();
        while (b < '!' || '~' < b) {
            b = read();
        }
        while ('!' <= b && b <= '~') {
            builder.appendCodePoint(b);
            b = read();
        }
        return builder.toString();
    }

    String nextLine() {
        StringBuilder builder = new StringBuilder();
        int b = read();
        while (b != 0 && b != '\r' && b != '\n') {
            builder.appendCodePoint(b);
            b = read();
        }
        if (b == '\r') {
            read();
        }
        return builder.toString();
    }

    int nextInt() {
        long val = nextLong();
        if ((int)val != val) {
            throw new NumberFormatException();
        }
        return (int)val;
    }

    long nextLong() {
        int b = read();
        while (b < '!' || '~' < b) {
            b = read();
        }
        boolean neg = false;
        if (b == '-') {
            neg = true;
            b = read();
        }
        long n = 0;
        int c = 0;
        while ('0' <= b && b <= '9') {
            n = n * 10 + b - '0';
            b = read();
            c++;
        }
        if (c == 0 || c >= 2 && n == 0) {
            throw new NumberFormatException();
        }
        return neg ? -n : n;
    }
}

class In {
    private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in), 0x10000);
    private StringTokenizer tokenizer;

    String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (IOException ignored) {
        }
        return tokenizer.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    char[] nextCharArray() {
        return next().toCharArray();
    }

    String[] nextStringArray(int n) {
        String[] s = new String[n];
        for (int i = 0; i < n; i++) {
            s[i] = next();
        }
        return s;
    }

    char[][] nextCharGrid(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

    int[][] nextIntMatrix(int h, int w) {
        int[][] a = new int[h][w];
        for (int i = 0; i < h; i++) {
            a[i] = nextIntArray(w);
        }
        return a;
    }

    long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }

    long[][] nextLongMatrix(int h, int w) {
        long[][] a = new long[h][w];
        for (int i = 0; i < h; i++) {
            a[i] = nextLongArray(w);
        }
        return a;
    }

    List<List<Integer>> nextEdges(int n, int m, boolean directed) {
        List<List<Integer>> res = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            res.add(new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int u = nextInt() - 1;
            int v = nextInt() - 1;
            res.get(u).add(v);
            if (!directed) {
                res.get(v).add(u);
            }
        }
        return res;
    }
}

class Out {
    private final PrintWriter out = new PrintWriter(System.out);
    private final PrintWriter err = new PrintWriter(System.err);
    boolean autoFlush = false;
    boolean enableDebug;

    Out(boolean enableDebug) {
        this.enableDebug = enableDebug;
    }

    void println(Object... args) {
        if (args == null || args.getClass() != Object[].class) {
            args = new Object[] {args};
        }
        out.println(Arrays.stream(args).map(obj -> {
            Class<?> clazz = obj == null ? null : obj.getClass();
            return clazz == Double.class ? String.format("%.10f", obj) :
                   clazz == byte[].class ? Arrays.toString((byte[])obj) :
                   clazz == short[].class ? Arrays.toString((short[])obj) :
                   clazz == int[].class ? Arrays.toString((int[])obj) :
                   clazz == long[].class ? Arrays.toString((long[])obj) :
                   clazz == char[].class ? Arrays.toString((char[])obj) :
                   clazz == float[].class ? Arrays.toString((float[])obj) :
                   clazz == double[].class ? Arrays.toString((double[])obj) :
                   clazz == boolean[].class ? Arrays.toString((boolean[])obj) :
                   obj instanceof Object[] ? Arrays.deepToString((Object[])obj) :
                   String.valueOf(obj);
        }).collect(Collectors.joining(" ")));
        if (autoFlush) {
            out.flush();
        }
    }

    void debug(Object... args) {
        if (!enableDebug) {
            return;
        }
        if (args == null || args.getClass() != Object[].class) {
            args = new Object[] {args};
        }
        err.println(Arrays.stream(args).map(obj -> {
            Class<?> clazz = obj == null ? null : obj.getClass();
            return clazz == Double.class ? String.format("%.10f", obj) :
                   clazz == byte[].class ? Arrays.toString((byte[])obj) :
                   clazz == short[].class ? Arrays.toString((short[])obj) :
                   clazz == int[].class ? Arrays.toString((int[])obj) :
                   clazz == long[].class ? Arrays.toString((long[])obj) :
                   clazz == char[].class ? Arrays.toString((char[])obj) :
                   clazz == float[].class ? Arrays.toString((float[])obj) :
                   clazz == double[].class ? Arrays.toString((double[])obj) :
                   clazz == boolean[].class ? Arrays.toString((boolean[])obj) :
                   obj instanceof Object[] ? Arrays.deepToString((Object[])obj) :
                   String.valueOf(obj);
        }).collect(Collectors.joining(" ")));
        err.flush();
    }

    void println(char a) {
        out.println(a);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(int a) {
        out.println(a);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(long a) {
        out.println(a);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(double a) {
        out.println(String.format("%.10f", a));
        if (autoFlush) {
            out.flush();
        }
    }

    void println(String s) {
        out.println(s);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(char[] s) {
        out.println(String.valueOf(s));
        if (autoFlush) {
            out.flush();
        }
    }

    void println(int[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (int i : a) {
            joiner.add(Integer.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(long[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (long i : a) {
            joiner.add(Long.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void flush() {
        err.flush();
        out.flush();
    }
}